The minimum-weight design of compressively loaded composite plates and composite stiffened panels under constrained post-buckling strength is addressed herein. A nonlinear finite element code, COSAP (COmposite Structural Analysis Program) was applied to analyze the buckling and postbuckling behavior. As an optimization technique, a modified Genetic Algorithm was used to find the optimum points. The parallel computing scheme was implemented with MPI (Message Passing Interface) library and realized in a parallel-computing supercomputer and a pc cluster. The optimal design was performed with two chosen examples: a composite plate and a composite stiffened panel. The design variables were the number of plies and the ply angle in each ply. In case of the stiffened panels, the size and the location of the stiffeners were also considered as the design variables. The objective function was defined as the product of the nondimensional weight and the strength. The optimization results showed better performances than conventional designs.