Examples of transversely isotropic materials include some piezoelectric materials (e.g. PZT-4, barium titanate) and fiber-reinforced composites where all fibers are in parallel.

The compliance matrix takes the form,

where .

The factor 2 multiplying the shear modulii in the compliance matrix results from the difference between shear strain and engineering shear strain, where , etc.

where,

The fact that the stiffness matrix is symmetric requires that the following statements hold,

The factor of 2 multiplying the shear modulii in the stiffness matrix results from the difference between shear strain and engineering shear strain, where , etc.