This paper presents the variationally consistent first-order shear deformation plate theory based on Hamilton’s principle. The governing partial differential equation of motion, in terms of shear deformation, is of the sixth order per x and y. An advanced plate theory satisfying force equilibrium, in terms of bending deflection, of the fourth order is also outlined. Illustrative examples are solved analytically and natural frequencies are compared with existing ones determined by the Rayleigh–Ritz method within the classical Mindlin thick plate theory. An evaluation of reliability of the considered two first-order shear deformation plate theories is given.