An elastic constant for the ratio of shear stress to shear strain. The shear modulus is one of the Lamé constants. It can be expressed mathematically as follows:

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.