The general, linearized, coupled magnetoelastic equations for arbitrarily anisotropic, magnetically saturated insulators, which were derived in a previous paper, are specialized to the important case of a homogeneous, static biasing state. The equations applicable in the special case of a material in cubic class m3m are determined from the more general ones. Consideration of the material constants known for yttrium iron garnet allows the equations to be simplified considerably because many terms are negligible compared to a few which dominate. These latter equations are applied in the determination of the solution for the thickness vibrations of an infinite cubic plate, which is magnetized to saturation along a cube edge, for two special orientations of the magnetization direction relative to the surface of the plate. In both cases the driving field is normal to the magnetization direction, and it is shown that the fundamental solutions of the differential equations are coupled at the traction‐free and exchange‐torque‐free surfaces of the plate. However, when the fundamental solutions are circularly polarized, only those solutions which have the same sense of circular polarization are coupled. It is further shown, in both instances, that this boundary coupling disappears when the exchange interaction is neglected. In an Appendix, the procedure used to determine the influence of material symmetry on the equations is compared with a more accurate procedure.