The present study deals with the investigation of buckling and postbuckling responses of functionally graded hybrid square plates which are symmetric about its mid plane. The cutouts of various sizes and shapes located at the center of the plate are considered. The plate is subjected to positive and negative in-plane shear loads. The boundary conditions used are simply supported on all the four edges of the plate. Three stacking sequences are considered to investigate the optimum stacking sequence at which the critical buckling and first failure loads are highest. Functionally graded hybrid plates (FH) subjected to negative in-plane shear load is more effective compared to plates subjected to positive in-plane shear load. Diamond shaped cutout with small sized perforation has the highest critical buckling and first ply failure loads amongst the FH plates with cutouts. It is observed that the direction of applied in-plane shear load, fiber stacking sequence; cutout shape and size substantially influence the strength and failure characteristics of functionally graded hybrid composite plates.