Abstract: The nonlinear dynamic and static analysis of rectangular plates with four free edges on elastic foundation is a rather complicated problem in the theory of plates. Until now the problem has not been studied.In this paper, the deflection and stress function in terms of trigonometrical function and polynomial expression are first proposed. They satisfy all boundary conditions on four free edges. Then Duffing equation is obtained using Galerkin method. A numerical example is given to verify the method-