Based on Mindlin's plate theory, free vibration of simply supported rectangular plates is investigated by using the method of superimposition. In this paper, for a simply supported edge the conditions are w=0, M_x=0, M_<xy>=0 on x=constant. Eigenvalues of four digit accuracy are pro-vided for a wide range of plate aspect ratios, thickness to width ratios, and modal shapes. Numerical results are compared with those of classical solutions.