The present paper is concerned with the cyclic inelastic large deflection analysis of structural steel members, such as pin-ended columns and fixed-ended tubular beam-columns of strut type. An elastoplastic finite element formulation for beam-columns, accounting for both the material and geometrical nonlinearities, was developed and implemented in the computer program FEAP used in the analysis. The geometrical nonlinearity is considered using the modified approximate updated Lagrangian description of motion. The two-surface plasticity model, recently developed by the authors, is employed for material nonlinearity. The model accounts for the important cyclic characteristics of structural steel, even within the yield plateau, such as, the decrease and disappearance of the yield plateau, reduction of the elastic range and cyclic strain hardening. The cyclic elastoplastic performance of the formulation was found to be good when compared with the experimental results as well as the results obtained from other material models