diff --git a/test/domains/continuum/test_hu_washizu_kernel.jl b/test/domains/continuum/test_hu_washizu_kernel.jl
new file mode 100644
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+++ b/test/domains/continuum/test_hu_washizu_kernel.jl
@@ -0,0 +1,132 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+`HuWashizuKernel`: three-field (u, ε̃, σ̃) on the DOF-based assembler.
+
+1. Strain–strain block matches `vol * M`.
+2. Strain–stress / stress–strain blocks match `−vol*G` and `+vol*G`.
+3. `K_uu`, `K_uε`, `K_εu`, `K_σσ` are zero.
+4. Coupling satisfies `K_uσ + K_σu^\\mathsf{T} \\approx 0` (symmetric global `K`).
+5. `assemble!` allocates 0 bytes after warmup.
+"""
+
+using Test
+using JuliaFEM
+using JuliaFEM: HuWashizuKernel, ContinuumFormulation, FullThreeD
+using JuliaFEM: DOFBasedCOOAssembler, DOFBasedCOOCache, assemble!, extract_system
+using JuliaFEM: create_unit_cube_mesh, create_elements!, @DOFSet, DOF, Displacement, Vertex
+using JuliaFEM: matrix_free_op
+using LinearAlgebra
+using SparseArrays
+using Tensors
+
+function _hex8_unit_cube_single_element()
+    return create_unit_cube_mesh(Hex8; nx = 1, ny = 1, nz = 1)
+end
+
+@testset "HuWashizuKernel Voigt blocks vs vol·M, vol·G" begin
+    mesh = _hex8_unit_cube_single_element()
+    mat = LinearElastic(E = 210e9, ν = 0.3)
+    S = @DOFSet{
+        u::DOF{Displacement{3}, Vertex},
+        eps::DOF{SymmetricTensor{2,3}, Cell},
+        sig::DOF{SymmetricTensor{2,3}, Cell},
+    }
+    elem, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
+    k = HuWashizuKernel(ContinuumFormulation{FullThreeD}(), mat)
+    asm = DOFBasedCOOAssembler()
+    cache = DOFBasedCOOCache(elem, handler, mesh, k)
+    assemble!(cache, asm, k, mesh)
+    K, _ = extract_system(cache)
+
+    n_u = 3 * length(mesh.nodes)
+    r_ε = (n_u + 1):(n_u + 6)
+    r_σ = (n_u + 7):(n_u + 12)
+    vol = 1.0
+
+    Kee = Matrix(K[r_ε, r_ε])
+    @test norm(Kee - vol * k.M) / max(norm(k.M), 1.0) < 1e-12
+
+    Kes = Matrix(K[r_ε, r_σ])
+    @test norm(Kes + vol * k.G) / max(norm(k.G), 1.0) < 1e-12
+
+    Kse = Matrix(K[r_σ, r_ε])
+    @test norm(Kse - vol * k.G) / max(norm(k.G), 1.0) < 1e-12
+end
+
+@testset "HuWashizuKernel empty blocks + u–σ skew coupling" begin
+    mesh = _hex8_unit_cube_single_element()
+    mat = LinearElastic(E = 210e9, ν = 0.3)
+    S = @DOFSet{
+        u::DOF{Displacement{3}, Vertex},
+        eps::DOF{SymmetricTensor{2,3}, Cell},
+        sig::DOF{SymmetricTensor{2,3}, Cell},
+    }
+    elem, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
+    k = HuWashizuKernel(ContinuumFormulation{FullThreeD}(), mat)
+    asm = DOFBasedCOOAssembler()
+    cache = DOFBasedCOOCache(elem, handler, mesh, k)
+    assemble!(cache, asm, k, mesh)
+    K, _ = extract_system(cache)
+
+    n_u = 3 * length(mesh.nodes)
+    r_u = 1:n_u
+    r_ε = (n_u + 1):(n_u + 6)
+    r_σ = (n_u + 7):(n_u + 12)
+
+    @test norm(K[r_u, r_u]) < 1e-14
+    @test norm(K[r_u, r_ε]) < 1e-14
+    @test norm(K[r_ε, r_u]) < 1e-14
+    @test norm(K[r_σ, r_σ]) < 1e-14
+
+    Kus = Matrix(K[r_u, r_σ])
+    Ksu = Matrix(K[r_σ, r_u])
+    skew = Kus + transpose(Ksu)
+    @test norm(skew) / max(norm(Kus), 1.0) < 1e-10
+
+    R = K - transpose(K)
+    @test norm(R) <= 1e-8 * max(1.0, norm(K))
+end
+
+@testset "HuWashizuKernel MatrixFreeOperator isposdef" begin
+    mesh = _hex8_unit_cube_single_element()
+    mat = LinearElastic(E = 210e9, ν = 0.3)
+    S = @DOFSet{
+        u::DOF{Displacement{3}, Vertex},
+        eps::DOF{SymmetricTensor{2,3}, Cell},
+        sig::DOF{SymmetricTensor{2,3}, Cell},
+    }
+    elem, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
+    k = HuWashizuKernel(ContinuumFormulation{FullThreeD}(), mat)
+    asm = DOFBasedCOOAssembler()
+    cache = DOFBasedCOOCache(elem, handler, mesh, k)
+    op = matrix_free_op(cache, asm, k, mesh)
+    @test LinearAlgebra.isposdef(op) == false
+end
+
+@testset "HuWashizuKernel assemble! zero allocations" begin
+    mesh = _hex8_unit_cube_single_element()
+    mat = LinearElastic(E = 210e9, ν = 0.3)
+    S = @DOFSet{
+        u::DOF{Displacement{3}, Vertex},
+        eps::DOF{SymmetricTensor{2,3}, Cell},
+        sig::DOF{SymmetricTensor{2,3}, Cell},
+    }
+    elem, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
+    k = HuWashizuKernel(ContinuumFormulation{FullThreeD}(), mat)
+    asm = DOFBasedCOOAssembler()
+    cache = DOFBasedCOOCache(elem, handler, mesh, k)
+    for _ in 1:3
+        assemble!(cache, asm, k, mesh)
+    end
+    GC.gc()
+    @test (@allocated assemble!(cache, asm, k, mesh)) == 0
+end
+
+@testset "HuWashizuKernel API guards" begin
+    mat = LinearElastic(E = 210e9, ν = 0.3)
+    k = HuWashizuKernel(ContinuumFormulation{FullThreeD}(), mat)
+    @test dofs_per_node(k) == 6
+    @test_throws ErrorException get_field(k)
+end