Presented are two optimality criterion techniques for the minimum weight design of mechanical and structural systems subject to limitations on stresses and natural frequencies. The results, based on their application to several examples, are compared with those obtained by other researchers and with standard nonlinear mathematical programming techniques, as well as with a special linear approach. It is shown in all cases that the optimality criterion methods are capable of locating the optimal design and are far superior to other methods in terms of computational time.