Design of steel tapered member under combined axial and flexural strength is somewhat complex if no approximations are made. However, recent Load Resistance Factor Design (LRFD) of the AISC code has treated the problem with sufficient accuracy and ease. The aim of this study is to present an algorithm for the optimum design of steel frames composed of tapered beams and columns with I-section in which the width is taken as constant, together with the thickness of web and flange, while the depth is considered to be varying linearly between joints .The objective function which is taken as the weight of the steel frame is expressed in terms of the depth at each joint. Both the displacement and combined axial and flexural strength constraints are considered in the formulation of the design problem .The strength constraints are expressed as a nonlinear function of the depth variables. The optimality criteria method is then used to obtain a recursive relationship for the depth variable under the displacement and strength constraints. Numerical examples are presented to demonstrate the practical application of the algorithm