The postbuckling behavior of a simply supported rectangular thick plate subjected to arbitrary loading conditions is investigated. The applied stress is taken to be a combination of a pure bending stress plus an extensional stress in the plane of the plate. Governing equations based on von Karman assumptions are used to solve the postbuckling problem by the Galerkin method. Buckling loads are obtained to compare with the results of Brunelle and Robertson. Postbuckled deflection is shown to increase with the transverse isotropic coefficient 5, and the effects of the in-plane bending stress are found to be quite significant for a thick plate.