In this paper, the governing equations and their boundary conditions of composite laminated plates are derived by means of Hamiltons principle based on a new simple third-order shear deformation theory.Especially, a simply supported rectangular symmetric cross-ply laminated composite plate subject to parametric excitation is taken into consideration.The method of multiple scales is utilized to obtain the approximate analytical solution for the principal parametrical resonance and the stability of the trivial solution of the system is analyzed.Finally, the numerical results have been compared with those of three-dimensional elasticity theory and J.N.Reddys theory.