A method is presented for optimum design of orthotropic composite laminated plates under in-plane loading with strength constraints. Ply orientation angles, ply thicknesses and numbers of the plies are chosen as design variables. Minimum of the plate thickness is used as the optimum criterion. A quadratic criterion of ply strength with different compression and tension strength is taken as the strength constraint. The directed sorting method with improving search by the method of conjugate directions is used to solve the problem. Numerical results are presented for different loading cases. The method results in a set of equivalent optimal structures for the given loads and the number of plies.