This paper has focused on vibration and buckling of thin rectangular plates when at least two opposite sides are simply supported condition and subjected to axial and biaxial initially stresses. Analysis is based on exact solution method, without further usage of any approximate method. First analytic techniques are used to discuss the free vibrations of plate. Then, natural frequencies and critical buckling loads are calculated. It is believed that in the present work, the exact closed form characteristic equations and their associated eigenfunctions for the considered six case are obtained for the first time.