Optimum structural design is formulated as a problem in nonlinear mathematical programming, i.e., a problem of selecting n design variables subject to m > n constraints such that an objective function is minimized. The design variables correspond to the geometrical or mechanical properties of the structural system, the constraints correspond to safety requirements such as limitations on stresses and deflections, and the objective function corresponds to weight or cost. The gradient projection method of nonlinear programming is described and an algorithm is presented for high-speed computation. Examples are presented in which the method is used to obtain least-weight designs of typical indeterminate rigid frames made of standard steel wide flange shapes. The examples illustrate that the programming approach affords a sound mathematical basis on which to develop rational methods of structural design.