A nonlinear analysis of the buckling and post-buckling responses of a simply supported laminated composite plate under an axial in-plane compressive load is presented. The model for symmetric cross-ply laminated composite plates made from various composite materials, such as, Graphite/Epoxy, Graphite/PEKK, Graphite/PEEK, and Kevlar/PEKK is given here. The governing equations of post-buckling composite plates with large strains are obtained by using the minimum total potential energy principle. The post-buckling behaviors of Graphite/Epoxy composite plate and toughened composite plates are studied by using this model. The critical buckling load and buckled position are determined. The stress and strain fields of the buckled composite plates are also determined. Buckling analysis is combined with failure analysis by applying Tsai-Hill theory. The effect of the toughened composites (matrix, or fibers or both) on the critical buckling load, post buckling behavior of the laminated composite plates are evaluated.