diff --git a/docs/src/tutorials/conic/ellipse_approx.jl b/docs/src/tutorials/conic/ellipse_approx.jl
index 81fbbf5082d..0d78f1f2722 100644
--- a/docs/src/tutorials/conic/ellipse_approx.jl
+++ b/docs/src/tutorials/conic/ellipse_approx.jl
@@ -109,7 +109,7 @@ m, n = size(S)
     [i in 1:m],
     S[i, :]' * Z * S[i, :] - 2 * S[i, :]' * z + s <= 1,
 )
-@constraint(model, [t; vec(Z)] in MOI.RootDetConeSquare(n))
+@constraint(model, (t, Z) in MOI.RootDetConeSquare(n))
 @objective(model, Max, t)
 optimize!(model)
 Test.@test termination_status(model) == OPTIMAL    #src
@@ -208,9 +208,11 @@ set_silent(model)
 ## The former constraint S[i, :]' * Z * S[i, :] - 2 * S[i, :]' * z + s <= 1
 f = [1 - S[i, :]' * Z * S[i, :] + 2 * S[i, :]' * z - s for i in 1:m]
 @constraint(model, f in MOI.Nonnegatives(m))
-## The former constraint [t; vec(Z)] in MOI.RootDetConeSquare(n)
-Z_upper = [Z[i, j] for j in 1:n for i in 1:j]
-@constraint(model, 1 * vcat(t, Z_upper) .+ 0 in MOI.RootDetConeTriangle(n))
+## The former constraint (t, Z) in MOI.RootDetConeSquare(n)
+@constraint(
+    model,
+    (1.0 * t, LinearAlgebra.Symmetric(1.0 .* Z)) in MOI.RootDetConeTriangle(n),
+)
 ## The former @objective(model, Max, t)
 @objective(model, Max, 1 * t + 0)
 optimize!(model)
diff --git a/docs/src/tutorials/conic/experiment_design.jl b/docs/src/tutorials/conic/experiment_design.jl
index 88edd583dc4..f4d61b05e8b 100644
--- a/docs/src/tutorials/conic/experiment_design.jl
+++ b/docs/src/tutorials/conic/experiment_design.jl
@@ -210,11 +210,8 @@ set_silent(dOpt)
 @variable(dOpt, t)
 @objective(dOpt, Max, t)
 @constraint(dOpt, sum(np) <= n)
-E = V * LinearAlgebra.diagm(0 => np ./ n) * V'
-@constraint(
-    dOpt,
-    [t, 1, (E[i, j] for i in 1:q for j in 1:i)...] in MOI.LogDetConeTriangle(q)
-)
+E = LinearAlgebra.Symmetric(V * LinearAlgebra.diagm(0 => np ./ n) * V')
+@constraint(dOpt, (t, 1.0, E) in MOI.LogDetConeTriangle(q))
 optimize!(dOpt)
 objective_value(dOpt)
 #-
diff --git a/docs/src/tutorials/conic/min_ellipse.jl b/docs/src/tutorials/conic/min_ellipse.jl
index 1fc33027a85..c934cced579 100644
--- a/docs/src/tutorials/conic/min_ellipse.jl
+++ b/docs/src/tutorials/conic/min_ellipse.jl
@@ -119,7 +119,7 @@ end
 # the conic reformulation:
 
 @variable(model, log_det_P)
-@constraint(model, [log_det_P; 1; vec(P²)] in MOI.LogDetConeSquare(n))
+@constraint(model, (log_det_P, 1, P²) in MOI.LogDetConeSquare(n))
 @objective(model, Max, log_det_P)
 
 # Now, solve the program:
diff --git a/docs/src/tutorials/conic/tips_and_tricks.jl b/docs/src/tutorials/conic/tips_and_tricks.jl
index 2471a19029b..2d7f7b46bdf 100644
--- a/docs/src/tutorials/conic/tips_and_tricks.jl
+++ b/docs/src/tutorials/conic/tips_and_tricks.jl
@@ -95,7 +95,7 @@ set_silent(model)
 @variable(model, x[1:3])
 @variable(model, t)
 @constraint(model, sum(x) == 1)
-@constraint(model, [t; x] in SecondOrderCone())
+@constraint(model, (t, x) in SecondOrderCone())
 @objective(model, Min, t)
 optimize!(model)
 value(t), value.(x)
@@ -117,7 +117,7 @@ set_silent(model)
 @variable(model, θ)
 @variable(model, t)
 @expression(model, residuals, θ * data .- target)
-@constraint(model, [t; 0.5; residuals] in RotatedSecondOrderCone())
+@constraint(model, (t, 0.5, residuals) in RotatedSecondOrderCone())
 @objective(model, Min, t)
 optimize!(model)
 value(θ), value(t)
@@ -140,7 +140,7 @@ set_silent(model)
 @variable(model, x == 1.5)
 @variable(model, z)
 @objective(model, Min, z)
-@constraint(model, [x, 1, z] in MOI.ExponentialCone())
+@constraint(model, (x, 1, z) in MOI.ExponentialCone())
 optimize!(model)
 value(z), exp(1.5)
 
@@ -153,7 +153,7 @@ set_silent(model)
 @variable(model, x)
 @variable(model, z == 1.5)
 @objective(model, Max, x)
-@constraint(model, [x, 1, z] in MOI.ExponentialCone())
+@constraint(model, (x, 1, z) in MOI.ExponentialCone())
 optimize!(model)
 value(x), log(1.5)
 
@@ -170,7 +170,7 @@ set_silent(model)
 @objective(model, Min, t)
 @variable(model, u[1:N])
 @constraint(model, sum(u) <= 1)
-@constraint(model, [i = 1:N], [x[i] - t, 1, u[i]] in MOI.ExponentialCone())
+@constraint(model, [i = 1:N], (x[i] - t, 1, u[i]) in MOI.ExponentialCone())
 optimize!(model)
 value(t), log(sum(exp.(x0)))
 
@@ -214,7 +214,7 @@ set_silent(model)
 @objective(model, Max, sum(t))
 @constraint(model, sum(x) == 1)
 @constraint(model, A * x .<= b)
-@constraint(model, [i = 1:n], [t[i], x[i], 1] in MOI.ExponentialCone())
+@constraint(model, [i = 1:n], (t[i], x[i], 1) in MOI.ExponentialCone())
 optimize!(model)
 objective_value(model)
 
@@ -232,7 +232,7 @@ set_silent(model)
 @objective(model, Max, -t)
 @constraint(model, sum(x) == 1)
 @constraint(model, A * x .<= b)
-@constraint(model, [t; ones(n); x] in MOI.RelativeEntropyCone(2n + 1))
+@constraint(model, (t, ones(n), x) in MOI.RelativeEntropyCone(2n + 1))
 optimize!(model)
 objective_value(model)
 
@@ -252,7 +252,7 @@ model = Model(SCS.Optimizer)
 set_silent(model)
 @variable(model, t)
 @variable(model, x >= 1.5)
-@constraint(model, [t, 1, x] in MOI.PowerCone(1 / 3))
+@constraint(model, (t, 1, x) in MOI.PowerCone(1 / 3))
 @objective(model, Min, t)
 optimize!(model)
 value(t), value(x)
@@ -273,7 +273,7 @@ function p_norm(x::Vector, p)
     set_silent(model)
     @variable(model, r[1:N])
     @variable(model, t)
-    @constraint(model, [i = 1:N], [r[i], t, x[i]] in MOI.PowerCone(1 / p))
+    @constraint(model, [i = 1:N], (r[i], t, x[i]) in MOI.PowerCone(1 / p))
     @constraint(model, sum(r) == t)
     @objective(model, Min, t)
     optimize!(model)
@@ -334,10 +334,64 @@ set_silent(model)
 @variable(model, x[1:4])
 @variable(model, t)
 @constraint(model, sum(x) == 1)
-@constraint(model, [t; x] in MOI.GeometricMeanCone(5))
+@constraint(model, (t, x) in MOI.GeometricMeanCone(5))
 optimize!(model)
 value(t), value.(x)
 
+# ## RootDetCone
+
+# The [`MOI.RootDetConeSquare`](@ref) is a cone of the form:
+# ```math
+# K = \{ (t, X) \in \mathbb{R}^{1+d^2} : t \le \det(X)^{\frac{1}{d}} \}
+# ```
+
+model = Model(SCS.Optimizer)
+set_silent(model)
+@variable(model, t)
+@variable(model, X[1:2, 1:2])
+@objective(model, Max, t)
+@constraint(model, (t, X) in MOI.RootDetConeSquare(2))
+@constraint(model, X .== [2 1; 1 3])
+optimize!(model)
+value(t), sqrt(LinearAlgebra.det(value.(X)))
+
+# If `X` is symmetric, then you can use [`MOI.RootDetConeTriangle`](@ref)
+# instead. This can be more efficient because the solver does not need to add
+# additional constraints to ensure `X` is symmetric.
+
+@constraint(
+    model,
+    (t, LinearAlgebra.Symmetric(X)) in MOI.RootDetConeTriangle(2),
+)
+
+# ## LogDetCone
+
+# The [`MOI.LogDetConeSquare`](@ref) is a cone of the form:
+# ```math
+# K = \{ (t, u, X) \in \mathbb{R}^{2+d^2} : t \le u \log(\det(X / u)) \}
+# ```
+
+model = Model(SCS.Optimizer)
+set_silent(model)
+@variable(model, t)
+@variable(model, u)
+@variable(model, X[1:2, 1:2])
+@objective(model, Max, t)
+@constraint(model, (t, u, X) in MOI.LogDetConeSquare(2))
+@constraint(model, X .== [2 1; 1 3])
+@constraint(model, u == 0.5)
+optimize!(model)
+value(t), 0.5 * log(LinearAlgebra.det(value.(X) ./ 0.5))
+
+# If `X` is symmetric, then you can use [`MOI.LogDetConeTriangle`](@ref)
+# instead. This can be more efficient because the solver does not need to add
+# additional constraints to ensure `X` is symmetric.
+
+@constraint(
+    model,
+    (t, u, LinearAlgebra.Symmetric(X)) in MOI.LogDetConeTriangle(2),
+)
+
 # ## Other Cones and Functions
 
 # For other cones supported by JuMP, check out the
diff --git a/src/print.jl b/src/print.jl
index ba03e5dccd7..fd97da8f1c1 100644
--- a/src/print.jl
+++ b/src/print.jl
@@ -696,6 +696,10 @@ function function_string(
     return str * "\\end{bmatrix}"
 end
 
+function function_string(mime::MIME, f::Tuple)
+    return string("(", join([function_string(mime, fi) for fi in f], ", "), ")")
+end
+
 function function_string(mode, constraint::AbstractConstraint)
     f = reshape_vector(jump_function(constraint), shape(constraint))
     return function_string(mode, f)
diff --git a/src/sd.jl b/src/sd.jl
index d409771d324..dae7be1a2c0 100644
--- a/src/sd.jl
+++ b/src/sd.jl
@@ -768,3 +768,120 @@ function build_variable(
     x = _vectorize_variables(_error, variables)
     return VariablesConstrainedOnCreation(x, set, SymmetricMatrixShape(n))
 end
+
+"""
+    TupleShape(args::Pair{<:AbstractShape,Int}...) <: AbstractShape
+
+A shape for representing tuple-valued functions, where each element of the tuple
+is a different [`AbstractShape`](@ref) mapped to the number of scalar elements
+in that shape.
+
+## Example
+
+```jldoctest
+julia> shape = TupleShape(ScalarShape() => 1, SymmetricMatrixShape(2) => 3);
+```
+"""
+struct TupleShape{T} <: AbstractShape
+    shapes::T
+    TupleShape(args::Pair{<:AbstractShape,Int}...) = new{typeof(args)}(args)
+end
+
+function vectorize(f::Tuple, shape::TupleShape)
+    vectors = [vectorize(fi, si[1]) for (fi, si) in zip(f, shape.shapes)]
+    return reduce(vcat, vectors)
+end
+
+reshape_set(set::MOI.AbstractVectorSet, ::TupleShape) = set
+
+function reshape_vector(v::Vector{T}, shape::TupleShape) where {T}
+    out = Any[]
+    offset = 0
+    for (s, dimension) in shape.shapes
+        push!(out, reshape_vector(v[offset.+(1:dimension)], s))
+        offset += dimension
+    end
+    return tuple(out...)
+end
+
+_shape_from_function(::Union{Real,AbstractJuMPScalar}) = ScalarShape() => 1
+_shape_from_function(x::AbstractVector) = VectorShape() => length(x)
+
+function build_constraint(
+    error_fn::Function,
+    f::Tuple,
+    set::Union{MOI.AbstractScalarSet,MOI.AbstractVectorSet},
+)
+    return error_fn(
+        "The tuple function $(typeof(f)) is not supported for a set of type " *
+        "$(typeof(set)).",
+    )
+end
+
+function build_constraint(
+    error_fn::Function,
+    f::Tuple{Vararg{Union{Real,AbstractJuMPScalar,AbstractVector}}},
+    set::MOI.AbstractVectorSet,
+)
+    shape = TupleShape(_shape_from_function.(f)...)
+    return VectorConstraint(vectorize(f, shape), set, shape)
+end
+
+function build_constraint(
+    error_fn::Function,
+    f::Tuple{<:Union{Real,AbstractJuMPScalar},<:LinearAlgebra.Symmetric},
+    set::MOI.RootDetConeTriangle,
+)
+    n = LinearAlgebra.checksquare(f[2])
+    shape = TupleShape(
+        ScalarShape() => 1,
+        SymmetricMatrixShape(n) => div(n * (n + 1), 2),
+    )
+    return VectorConstraint(vectorize(f, shape), set, shape)
+end
+
+function build_constraint(
+    error_fn::Function,
+    f::Tuple{<:Union{Real,AbstractJuMPScalar},<:AbstractMatrix},
+    set::MOI.RootDetConeSquare,
+)
+    n = LinearAlgebra.checksquare(f[2])
+    shape = TupleShape(ScalarShape() => 1, SquareMatrixShape(n) => n^2)
+    return VectorConstraint(vectorize(f, shape), set, shape)
+end
+
+function build_constraint(
+    error_fn::Function,
+    f::Tuple{
+        <:Union{Real,AbstractJuMPScalar},
+        <:Union{Real,AbstractJuMPScalar},
+        <:LinearAlgebra.Symmetric,
+    },
+    set::MOI.LogDetConeTriangle,
+)
+    n = LinearAlgebra.checksquare(f[3])
+    shape = TupleShape(
+        ScalarShape() => 1,
+        ScalarShape() => 1,
+        SymmetricMatrixShape(n) => div(n * (n + 1), 2),
+    )
+    return VectorConstraint(vectorize(f, shape), set, shape)
+end
+
+function build_constraint(
+    error_fn::Function,
+    f::Tuple{
+        <:Union{Real,AbstractJuMPScalar},
+        <:Union{Real,AbstractJuMPScalar},
+        <:AbstractMatrix,
+    },
+    set::MOI.LogDetConeSquare,
+)
+    n = LinearAlgebra.checksquare(f[3])
+    shape = TupleShape(
+        ScalarShape() => 1,
+        ScalarShape() => 1,
+        SquareMatrixShape(n) => n^2,
+    )
+    return VectorConstraint(vectorize(f, shape), set, shape)
+end
diff --git a/src/sets.jl b/src/sets.jl
index e5651338fdf..a283cd7a782 100644
--- a/src/sets.jl
+++ b/src/sets.jl
@@ -41,6 +41,16 @@ function build_constraint(
     return build_constraint(_error, func, moi_set(set, length(func)))
 end
 
+function build_constraint(
+    error_fn::Function,
+    f::Tuple{Vararg{Union{Real,AbstractJuMPScalar,AbstractVector},N}},
+    set::AbstractVectorSet,
+) where {N}
+    shape = TupleShape(_shape_from_function.(f)...)
+    args = vectorize(f, shape)
+    return VectorConstraint(args, moi_set(set, length(args)), shape)
+end
+
 """
     build_constraint(
         _error::Function,
diff --git a/src/shapes.jl b/src/shapes.jl
index 62d1472db70..1e0693f04ad 100644
--- a/src/shapes.jl
+++ b/src/shapes.jl
@@ -112,6 +112,8 @@ Shape of scalar constraints.
 """
 struct ScalarShape <: AbstractShape end
 reshape_vector(α, ::ScalarShape) = α
+reshape_vector(x::Vector, ::ScalarShape) = first(x)
+vectorize(x, ::ScalarShape) = x
 
 """
     VectorShape
diff --git a/test/test_constraint.jl b/test/test_constraint.jl
index 16f256baade..44b2d3dc3c2 100644
--- a/test/test_constraint.jl
+++ b/test/test_constraint.jl
@@ -1710,4 +1710,93 @@ function test_eltype_for_constraint_primal_complex_float64()
     return
 end
 
+function test_tuple_shape_vector()
+    model = Model()
+    @variable(model, t)
+    @variable(model, x[1:3])
+    @variable(model, u)
+    @variable(model, v)
+    @variable(model, w)
+    for set in (
+        MOI.ExponentialCone(),
+        MOI.DualExponentialCone(),
+        MOI.PowerCone(0.5),
+        MOI.DualPowerCone(0.5),
+    )
+        c = @constraint(model, (u, v, w) in set)
+        obj = constraint_object(c)
+        @test obj.func == [u, v, w]
+        @test reshape_vector(obj.func, obj.shape) == (u, v, w)
+        @test reshape_set(obj.set, obj.shape) == obj.set
+    end
+    for set in
+        (MOI.SecondOrderCone(4), SecondOrderCone(), MOI.GeometricMeanCone(4))
+        c = @constraint(model, (t, x) in set)
+        obj = constraint_object(c)
+        @test obj.func == [t; x]
+        @test reshape_vector(obj.func, obj.shape) == (t, x)
+        @test reshape_set(obj.set, obj.shape) == obj.set
+    end
+    for set in (MOI.RotatedSecondOrderCone(5), RotatedSecondOrderCone())
+        c = @constraint(model, (t, u, x) in set)
+        obj = constraint_object(c)
+        @test obj.func == [t; u; x]
+        @test reshape_vector(obj.func, obj.shape) == (t, u, x)
+        @test reshape_set(obj.set, obj.shape) == obj.set
+    end
+    return
+end
+
+function test_tuple_shape_det_cone()
+    model = Model()
+    @variable(model, t)
+    @variable(model, u)
+    @variable(model, X[1:2, 1:2])
+    Y = LinearAlgebra.Symmetric(X)
+    U = [X[i, j] for j in 1:2 for i in 1:j]
+    c = @constraint(model, (t, X) in MOI.RootDetConeSquare(2))
+    obj = constraint_object(c)
+    @test obj.func == [t; vec(X)]
+    @test reshape_vector(obj.func, obj.shape) == (t, X)
+    @test reshape_set(obj.set, obj.shape) == obj.set
+    c = @constraint(model, (t, Y) in MOI.RootDetConeTriangle(2))
+    obj = constraint_object(c)
+    @test obj.func == [t; U]
+    @test reshape_vector(obj.func, obj.shape) == (t, Y)
+    @test reshape_set(obj.set, obj.shape) == obj.set
+    c = @constraint(model, (t, u, X) in MOI.LogDetConeSquare(2))
+    obj = constraint_object(c)
+    @test obj.func == [t; u; vec(X)]
+    @test reshape_vector(obj.func, obj.shape) == (t, u, X)
+    @test reshape_set(obj.set, obj.shape) == obj.set
+    c = @constraint(model, (t, u, Y) in MOI.LogDetConeTriangle(2))
+    obj = constraint_object(c)
+    @test obj.func == [t; u; U]
+    @test reshape_vector(obj.func, obj.shape) == (t, u, Y)
+    @test reshape_set(obj.set, obj.shape) == obj.set
+    return
+end
+
+function test_tuple_shape_unsupported_error()
+    model = Model()
+    @variable(model, t)
+    @variable(model, x[1:2])
+    err = ErrorException(
+        "In `@constraint(model, (t,) in MOI.ZeroOne())`: " *
+        "The tuple function $(Tuple{VariableRef}) is not supported for " *
+        "a set of type $(MOI.ZeroOne).",
+    )
+    @test_throws_strip err @constraint(model, (t,) in MOI.ZeroOne())
+    err = ErrorException(
+        "In `@constraint(model, ((x[1], x[2]),) in MOI.SOS1([1.0, 2.0]))`: " *
+        "The tuple function $(Tuple{Tuple{VariableRef, VariableRef}}) is not " *
+        "supported for a set of type $(MOI.SOS1{Float64}).",
+    )
+    @test_throws_strip(
+        err,
+        @constraint(model, ((x[1], x[2]),) in MOI.SOS1([1.0, 2.0])),
+    )
+    return
+end
+
 end
diff --git a/test/test_print.jl b/test/test_print.jl
index 790db8a1c40..77849b44fec 100644
--- a/test/test_print.jl
+++ b/test/test_print.jl
@@ -877,6 +877,20 @@ function test_print_hermitian_psd_cone()
     return
 end
 
+function test_print_rootdetcone()
+    model = Model()
+    @variable(model, t)
+    @variable(model, X[1:2, 1:2], Symmetric)
+    in_sym = JuMP._math_symbol(MIME("text/plain"), :in)
+    set = MOI.RootDetConeTriangle(2)
+    c = @constraint(model, (t, X) in set)
+    @test sprint(io -> show(io, MIME("text/plain"), c)) ==
+          "(t, [X[1,1]  X[1,2];\n X[1,2]  X[2,2]]) $in_sym $set"
+    @test sprint(io -> show(io, MIME("text/latex"), c)) ==
+          "\$\$ (t, \\begin{bmatrix}\nX_{1,1} & X_{1,2}\\\\\n\\cdot & X_{2,2}\\\\\n\\end{bmatrix}) \\in \\text{$set} \$\$"
+    return
+end
+
 function test_print_complex_string_round()
     @test JuMP._string_round(1.0 + 0.0im) == "1"
     @test JuMP._string_round(-1.0 + 0.0im) == "-1"