diff --git a/test/domains/continuum/test_continuum_brick_solve.jl b/test/domains/continuum/test_continuum_brick_solve.jl
new file mode 100644
index 0000000..25b0175
--- /dev/null
+++ b/test/domains/continuum/test_continuum_brick_solve.jl
@@ -0,0 +1,43 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+"""
+Small `Hex8` brick: `ContinuumKernel` + `PenaltyDirichlet` on `xmin` + nodal
+`z` load, direct sparse solve, relative residual check.
+"""
+
+using Test
+using JuliaFEM
+using JuliaFEM: ContinuumKernel, ContinuumFormulation, FullThreeD, LinearElastic
+using JuliaFEM: DOFBasedCOOAssembler, DOFBasedCOOCache, assemble!, extract_system
+using JuliaFEM: PenaltyDirichlet, apply_constraint!, apply_load!, NodalForce
+using JuliaFEM: @DOFSet, DOF, Displacement, Vertex, Hex8
+using LinearAlgebra
+
+include("solve_brick_helpers.jl")
+
+@testset "ContinuumKernel: brick direct solve (xmin fixed + uz load)" begin
+    mesh = brick_hex_mesh(2, 2, 2)
+    S = @DOFSet{u::DOF{Displacement{3}, Vertex}}
+    elements, handler = create_elements!(mesh, Element{Hex8, Lagrange{1}, S})
+    kernel = ContinuumKernel(ContinuumFormulation{FullThreeD}(), LinearElastic(E = 210e9, ν = 0.3))
+    asm = DOFBasedCOOAssembler()
+    cache = DOFBasedCOOCache(elements, handler, mesh, kernel)
+    assemble!(cache, asm, kernel, mesh)
+    K, f = extract_system(cache)
+    fill!(f, 0.0)
+
+    u_fix = collect_vertex_dofs_on_nodeset(handler, mesh, :xmin)
+    uz = interior_uz_dof_index(handler, mesh)
+    λ = 1.0e14
+    bc = PenaltyDirichlet(u_fix, zeros(Float64, length(u_fix)); penalty = λ)
+    apply_load!(f, NodalForce([uz], [1.0e4]), cache, asm, kernel, mesh)
+
+    Kc = copy(K)
+    apply_constraint!(Kc, bc)
+    uc = Kc \ f
+    @test all(isfinite, uc)
+    ru = norm(Kc * uc - f) / max(norm(f), 1.0)
+    @test ru < 1.0e-8
+    @test maximum(abs.(uc[u_fix])) < 1.0e-4
+end