Two theories of shear deformable plate vibrations that account for the influence of the transverse normal stress component are derived. The first is a slightly modified Mindlin theory, including a shear correction factor, while in the second the use of the shear correction factor is replaced by stress components that exactly satisfy elasticity motion equations and plate face boundary conditions. A comparison with the exact 3D solution for a sinusoidally loaded rectangular plate and infinite strip is made. It is found that the refined theories significantly increase the accuracy of results compared to the original Mindlin theory.