Abstract This paper presents an efficient algorithm for both limit and shakedown analysis of 3-D steel frames by the kinematic method using linear programming technique. Several features in the application of linear programming for rigid-plastic analysis of three-dimensional steel frames are discussed, as: change of the variables, automatic choice of the initial basic matrix for the simplex algorithm, direct calculation of the dual variables by primal–dual technique. Some numerical examples are presented to demonstrate the robustness, efficiency of the proposed technique and computer program.