Using the specific values of  in matrix ,  it can be shown that the fourth-rank elasticity stiffness tensor may be written in 2-index Voigt notation as the matrix
The elasticity stiffness matrix  has 5 independent constants, which are related to well known engineering elastic moduli in the following way. These engineering moduli are experimentally determined.
The compliance matrix (inverse of the elastic stiffness matrix) is
where .  In engineering notation, 
Comparing these two forms of the compliance matrix shows us that the longitudinal Young's modulus is given by
Similarly, the transverse Young's modulus is 
The inplane shear modulus is
and the Poisson's ratio for loading along the polar axis is
Here, L represents the longitudinal (polar) direction and T represents the transverse direction.