A minimum-weight optimum design procedure is proposed including the reliabilities of various elements in a structure as constraints. The reliability indices corresponding to the various limit states are computed using the Stochastic Finite Element Method, and are required to be within a desired narrow range. A derivative-free constrained optimization algorithm with variable discrete step sizes is used to obtain the optimum design. Both serviceability and ultimate limit states can be incorporated; also, different levels of risk can be assigned to different limit states indicating their relative importance. The procedure can include system reliability constraints, has options for the addition or deletion of constraints, and can use design groups of similar members for computational efficiency.