Isotropy means independence of direction. An isotropic material can be described with two parameters, the Young’s modulus , and the Poisson’s ratio , which are the same in all directions. In the isotropic case there are only two independent elastic coefficients: or alternatively, the Lamé parameters .

For this approximation, the full 6x6 elasticity tensor is matched against the matrix for the isotropic symmetry class (see the section about Elasticity theory). From an isotropic stiffness tensor, the parameters or can be calculated as described below.

The Lamé parameters (Shear Modulus) and (Lamé Modulus) are found by calculating:

From the values of and , the estimates for the effective Young’s modulus () and effective Poisson’s ratio () are computed as:

Other engineering constants can also be obtained by transformation formulas (given e.g., by the Wikipedia page on Hooke's Law).

For the isotropic and transversely isotropic structures, the Isotropic Approximation for Strain Equivalence look as follows:

Comparing the full anisotropic stiffness matrix with the isotropic approximation, the known structure characteristics are confirmed: the approximated isotropic stiffness values fit well to the corresponding values in the full anisotropic stiffness tensor. But for the transversely isotropic case there is a discrepancy between the approximated isotropic stiffness tensor and the full anisotropic one: