One of two elastic constants named for French mathematician Gabriel Lamé (1795 to 1870). The first Lamé constant is λ, the bulk modulus (K) less two-thirds of the shear modulus (μ):

λ = K − (2/3)μ

The second Lamé constant is the shear modulus (μ):

μ = τ / γ = (ΔF/A) / (ΔL/L),

where
μ = Shear modulus
τ = Shear stress = ΔF/A
ΔF = Increment of shear force A = Area acted on by the shear force
γ = Shear strain = ΔL/L
ΔL = Increment of transverse displacement parallel to A L = Original length.

Lamé constants derived from elastic-wave velocities:

λ = ρ(V_{P}^{2} − 2V_{S}^{2})

μ = ρV_{S}^{2}

λ/μ = (V_{P}/V_{S})^{2} − 2,

where
λ = Lamé's first constant
μ = Lamé's second constant, the shear modulus V_{P} = Compressional-wave (P-wave) velocity V_{S} = Shear-wave (S-wave) velocity
ρ = Density.