A set of nonlinear equations describing the vibrations of sandwich plates is derived. These equations are then applied to a plate vibrating in plane strain and to a rectangular plate; with the boundary edges assumed to be hinged in both cases. It is shown that the nonlinear frequencies increase with the amplitude of vibration. It is shown also that transverse shear deformations play an important role; however the effect produced by these deformations decreases with increasing amplitudes of vibration.