Abstract: The stiffness constrained optimum design of composite laminates is studied. The structural weight is chosen to be the objective function, which is minimized under the stiffness and gauge constraints.The lamina thickness distribution is described by a biquadratic polynomial, whose six coefficients are chosen to be the design variables. The stiffness analysis is performed by the finite element method, in which a triangular element considering the transverse shear effects is used. The optimum problem is solved with the constrained variable metric method. A trapezoid composite laminate is designed.