The design of steel tapered members for combined axial and flexural strength is somewhat complex and tedious if no approximation is made. However, recent load and resistance factor design (LRFD) of the AISC code has treated the problem with sufficient accuracy and ease. In this study, an algorithm is developed for the optimum design of steel frames composed of prismatic and,'or tapered members. The width of an I-section is taken as constant, together with the thickness of web and flange, while the depth is considered to be varying linearly between joints. The depth at each joint in the frame where the lateral restraints are assumed to be provided is treated as a design variable. The objective function which is taken as the volume of the frame is expressed in terms of the depth at each joint. The displacement and combined axial and flexural strength constraints are considered in the formulation of the design problem. The strength constraints, which take into account the lateral torsional bucking resistance of the members between the adjacent lateral restraints, are expressed as an nonlinear function of the depth variables. The optimality criteria method is then used to obtain a recursive relationship for the depth variables under the displacement and strength constraints. These relationships are derived from the Kuhn-Tucker necessary conditions. The algorithm basically consists of two steps. In the first one, the frame is analysed under the external and unit loadings for the current values of the design variables. In the second, I:his response is utilized together with the values of Lagrange multipliers to compute the new values of the depth variables. This process is continued until convergence is obtained. Numerical examples are presented to demonstrate the practical application of the algorithm.