Abstract: The buckling of thin rectangular plates with various combinations of boundary conditions is studied, whose cosine-distributed compressive loads are applied along two opposite plate edges. On the basis of the symplectic elasticity in plane rectangular domain under symmetrical deformation, precise in-plane stress distribution is given. The buckling loads of the thin rectangular plates are analyzed by using the Galerkin method. After applying various combinations of boundary conditions, with the help of the symbolic computational software Maple, the Maple user program for calculating buckling loads is prepared. Nine combinations of boundary conditions are considered. The buckling coefficients are gained for thin rectangular elastic plates with various aspect ratios. The efficiency and validity of the proposed method are confirmed by a comparison with the published results. It can be concluded that the proposed method could provide a new way for the buckling analysis of thin rectangular plates subjected nonlinearly distributed in-plane loadings.