The governing equations for a ferroelectro-magnetic material are presented along with a proof of solution uniqueness. The equations for the general coupling coefficients (i.e. electro-magnetic, electro-mechanical, and magneto-mechanical) are provided. An analytical solution for a two-dimensional (plane-stress), transversely isotropic is presented. An effective coupling coefficient for determining the ability of a ferroelectro-magnetic material to convert and store input energies between different states is described.