diff --git a/src/MiniZinc.jl b/src/MiniZinc.jl
index 625fa04..c98cd47 100644
--- a/src/MiniZinc.jl
+++ b/src/MiniZinc.jl
@@ -15,11 +15,20 @@ const ReifiedEqualTo{T} = MOI.Reified{MOI.EqualTo{T}}
 const ReifiedBinPacking{T} = MOI.Reified{MOI.BinPacking{T}}
 const ReifiedTable{T} = MOI.Reified{MOI.Table{T}}
 
+struct MiniZincSet <: MOI.AbstractVectorSet
+    name::String
+    fields::Vector{Union{Int,UnitRange{Int}}}
+end
+
+MOI.dimension(set::MiniZincSet) = maximum(maximum, set.fields)
+Base.copy(set::MiniZincSet) = set
+
 MOI.Utilities.@model(
     Model,
     (MOI.ZeroOne, MOI.Integer, MOI.EqualTo{Bool}),
     (MOI.EqualTo, MOI.GreaterThan, MOI.LessThan, MOI.Interval),
     (
+        MiniZincSet,
         MOI.AllDifferent,
         MOI.Circuit,
         MOI.CountAtLeast,
diff --git a/src/write.jl b/src/write.jl
index 61f5982..88ab631 100644
--- a/src/write.jl
+++ b/src/write.jl
@@ -149,9 +149,17 @@ function _to_string(
     return ret
 end
 
-struct MiniZincSet <: MOI.AbstractSet
-    name::String
-    fields::Vector{Union{Int,UnitRange{Int}}}
+function _write_constraint(
+    io::IO,
+    predicates::Set,
+    variables::Dict,
+    f::MOI.VectorOfVariables,
+    mzn::MiniZincSet,
+)
+    strs = [_to_string(variables, f.variables[field]) for field in mzn.fields]
+    println(io, "constraint $(mzn.name)(", join(strs, ", "), ");")
+    push!(predicates, mzn.name)
+    return
 end
 
 function _write_constraint(
@@ -167,10 +175,7 @@ function _write_constraint(
         MOI.Circuit,
     },
 )
-    mzn = MiniZincSet(s)
-    strs = [_to_string(variables, f.variables[field]) for field in mzn.fields]
-    println(io, "constraint $(mzn.name)(", join(strs, ", "), ");")
-    push!(predicates, mzn.name)
+    _write_constraint(io, predicates, variables, f, MiniZincSet(s))
     return
 end
 
diff --git a/test/examples/packing.jl b/test/examples/packing.jl
new file mode 100644
index 0000000..cb664c1
--- /dev/null
+++ b/test/examples/packing.jl
@@ -0,0 +1,49 @@
+# Copyright (c) 2022 MiniZinc.jl contributors
+#
+# Use of this source code is governed by an MIT-style license that can be found
+# in the LICENSE.md file or at https://opensource.org/licenses/MIT.
+
+# Inspired from the square packing tutorial in https://www.minizinc.org/
+function test_packing()
+    n = 6
+    sizes = collect(1:n)
+    upper_bound = sum(sizes)
+    model = MOI.instantiate(
+        () -> MiniZinc.Optimizer{Int}("chuffed");
+        with_cache_type = Int,
+        with_bridge_type = Int,
+    )
+    MOI.set(model, MOI.RawOptimizerAttribute("model_filename"), "test.mzn")
+    # We need this `s` variable that is trivially equal to `sizes`
+    # because `MiniZincSet` supports only VectorOfVariables
+    s = [MOI.add_constrained_variable(model, MOI.Integer())[1] for i in 1:n]
+    x = [MOI.add_constrained_variable(model, MOI.Integer())[1] for i in 1:n]
+    y = [MOI.add_constrained_variable(model, MOI.Integer())[1] for i in 1:n]
+    max_x, _ = MOI.add_constrained_variable(model, MOI.Integer())
+    max_y, _ = MOI.add_constrained_variable(model, MOI.Integer())
+    MOI.add_constraint.(model, s, MOI.EqualTo.(sizes))
+    MOI.add_constraint.(model, x, MOI.Interval(1, upper_bound))
+    MOI.add_constraint.(model, y, MOI.Interval(1, upper_bound))
+    MOI.add_constraint(model, max_x, MOI.Interval(1, upper_bound))
+    MOI.add_constraint(model, max_y, MOI.Interval(1, upper_bound))
+    MOI.add_constraint.(model, 1max_x .- 1x, MOI.GreaterThan.(sizes))
+    MOI.add_constraint.(model, 1max_y .- 1y, MOI.GreaterThan.(sizes))
+    MOI.add_constraint(
+        model,
+        MOI.VectorOfVariables([x; y; s; s]),
+        MiniZinc.MiniZincSet(
+            "diffn",
+            [1:n, n .+ (1:n), 2n .+ (1:n), 3n .+ (1:n)],
+        ),
+    )
+    MOI.set(model, MOI.ObjectiveSense(), MOI.MIN_SENSE)
+    obj = (1max_x) * max_y
+    MOI.set(model, MOI.ObjectiveFunction{typeof(obj)}(), obj)
+    MOI.optimize!(model)
+    @test MOI.get(model, MOI.TerminationStatus()) === MOI.OPTIMAL
+    @test MOI.get(model, MOI.PrimalStatus()) === MOI.FEASIBLE_POINT
+    @test MOI.get(model, MOI.ResultCount()) == 1
+    @test MOI.get(model, MOI.ObjectiveValue()) == 120
+    rm("test.mzn")
+    return
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index a4502a6..96d6515 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1696,6 +1696,14 @@ function test_integer_bounds_less_than_than()
     index_map, _ = MOI.optimize!(mzn, model)
     @test MOI.get(mzn, MOI.TerminationStatus()) == MOI.OPTIMAL
     @test MOI.get(mzn, MOI.VariablePrimal(), index_map[x]) == 1
+end
+
+function test_minizincset()
+    set = MiniZinc.MiniZincSet("diffn", [1:2, 3:4, 5:6, 7:8])
+    @test MOI.dimension(set) == 8
+    model = MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}())
+    x, _ = MOI.add_constrained_variables(model, set)
+    @test length(x) == 8
     return
 end