A system of plate equations for the thickness‐shear and flexural vibrations superposed on large initial deflection due to bending is derived; in the stress–strain relations the terms associated with the fourth‐order elastic stiffness coefficients are retained. An explicit formula for the change in the fundamental cutoff thickness shear frequency is obtained and the effects of the terms associated with the fourth‐order constrants appear to be significant for large gradients of the rotation angles.