The elasto-plastic behavior of steel structures under cyclic loading is one of the significant subjects to estimate design criteria and design procedures based on the ultimate state. Analyzing the cyclic response of steel structures, it is necessary to estimate a mechanical model which can represent well a cyclic stress-strain relationship of steel and numerical techniques for the solution of non-linear structure problem. In this paper, we propose a solution method for an elasto-plastic large deformation analysis under uniaxial cyclic loading, which introduces a new iteration technique of minimizing the residual displacements for correcting residual force and a modified two-surface model as a constitutive equation. A few numerical simulations are presented to show the accuracy and efficiency of the proposed method.