A based on an optimality criterion is presented for designing minimum weight fiber reinforced composite structures with stress and displacement constraints. A recurrence relation based on an optimality criterion is used to modify the design variables during the iterative procedure. The displacement method of finite element analysis is used to determine the response of the structure to the applied loads. The method takes into consideration the effects of multiple displacement constraints, multiple loading conditions, and variable allowable stresses. Illustrative examples are given to show the application of the method to structures with certain displacements and twist specified, a problem basic to the developing technology of aeroelastic tailoring.