diff --git a/src/materials/symmetric_fourth_identity.jl b/src/materials/symmetric_fourth_identity.jl
new file mode 100644
index 0000000..7f2af76
--- /dev/null
+++ b/src/materials/symmetric_fourth_identity.jl
@@ -0,0 +1,10 @@
+# SPDX-FileCopyrightText: 2015-2026 Jukka Aho
+# SPDX-License-Identifier: MIT
+
+using Tensors
+
+"""Fourth-order symmetric identity 𝕀ˢʸᵐ for Lamé-style stiffness `λ I⊗I + 2μ 𝕀ˢʸᵐ`."""
+@inline function symmetric_identity_tensor()
+    return SymmetricTensor{4,3}((i, j, k, l) ->
+        (i == k && j == l ? 0.5 : 0.0) + (i == l && j == k ? 0.5 : 0.0))
+end