diff --git a/test/materials/test_j2_isotropic_plasticity.jl b/test/materials/test_j2_isotropic_plasticity.jl
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+++ b/test/materials/test_j2_isotropic_plasticity.jl
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+# SPDX-FileCopyrightText: 2015-2026 Jukka Aho
+# SPDX-License-Identifier: MIT
+
+using Test
+using JuliaFEM
+using Tensors
+
+@testset "J2LinearIsotropicPlasticity" begin
+    @testset "traits and state layout (no backstress)" begin
+        mat = J2LinearIsotropicPlasticity(E = 210e9, ν = 0.3, σ_y0 = 250e6, H_iso = 1e9)
+        @test material_behavior(mat) isa StatefulStrainDependent
+        @test required_state_variables(mat) === (PlasticStrain, EquivalentPlasticStrain)
+        _, _, st = compute_stress(mat, zero(SymmetricTensor{2,3}), NamedTuple(), 0.0)
+        @test !haskey(st, :α)
+    end
+
+    @testset "von Mises stress on yield surface" begin
+        mat = J2LinearIsotropicPlasticity(E = 210e9, ν = 0.3, σ_y0 = 250e6, H_iso = 2e9)
+        ε = SymmetricTensor{2,3}((0.008, 0.0, 0.0, 0.0, 0.0, 0.0))
+        σ, _, st = compute_stress(mat, ε, NamedTuple(), 0.0)
+        s = dev(σ)
+        seq = √(3 / 2) * √(s ⊡ s)
+        σ_y = mat.σ_y0 + mat.H_iso * st.κ
+        @test seq ≈ σ_y rtol = 1e-6
+    end
+
+    @testset "distinct from kinematic PerfectPlasticity (stress path)" begin
+        E = 210e9
+        ν = 0.3
+        σ_y = 250e6
+        H = 1e9
+        ε_load = SymmetricTensor{2,3}((0.006, 0.0, 0.0, 0.0, 0.0, 0.0))
+
+        mk = PerfectPlasticity(E = E, ν = ν, σ_y = σ_y, H = H)
+        mi = J2LinearIsotropicPlasticity(E = E, ν = ν, σ_y0 = σ_y, H_iso = H)
+
+        σk, _, _ = compute_stress(mk, ε_load, NamedTuple(), 0.0)
+        σi, _, _ = compute_stress(mi, ε_load, NamedTuple(), 0.0)
+        @test σk ≠ σi
+    end
+end