Abstract: The buckling and post-buckling behaviour of simply-supported ortho-tropic rectangular plates subjected to compressive forces along two opposite edges in the mid-plane is studied in this paper. The stability region of the load is obtained and it is shown that the critical load is at most double. By using the perturbation method with double parameters the asymptotic solution of the buckled state near the critical load is given, the possible buckled states and the dependence of them on parameters are analysed ...