In the nonlinear elastoplastic finite element analysis, the stresses must be updated at each Gauss point of the elements in each iteration of each load increment by a stress-updating process. The stress-updating process is performed by integrating of the constitutive equations in plasticity. It should be noted that the accuracy of the integrating the constitutive equations highly affects the accuracy of the final results of the structural analysis. In this study, the von-Mises plasticity model along with the isotropic and kinematic hardening mechanisms is considered in the small strain realm. The constitutive equations are converted to a nonlinear equation system in an augmented stress space. The aforementioned nonlinear equation system is solved by an semi implicit technique. The precision of the solution is depended to the radius of the yield surface which is used in the process of the solution. Therefore, the relations are derived so that one can pick up the yield surface radius from each arbitrary part of plasticity step. Finally, to determine the best time of loading step for calculating the radius of the yield surface, the a broad range of numerical tests is performed.