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This paper extends the smoothed finite element method (S-FEM) to the contact problems of elastic-plastic materials. Although the traditional one-pass node-to-segment (NTS) algorithm has been widely used, it may lead to challenges such as poor convergence rates of contact nonlinear system equations, inaccurate contact stress distribution, and errors that do not decrease with mesh refinement. Also, it cannot rigorously pass the contact patch test. By introducing a more sophisticated area regularization technique, these shortcomings are greatly improved, and can pass the contact patch test. Furthermore, the Newton-Raphson iteration procedures for solving elastic-plastic material contact problems achieves quadratic convergence rates. By utilizing information from neighboring elements, the SFEM technique converts the strain calculation of elements into that of the smoothting domains, further improving the robustness and convergence rate of the algorithm. Additionally, SFEM expands the space for numerical performance due to not using the Jacobian matrix obtained through coordinate mapping. With only minor modifications to the traditional FEM program architecture, a correct implementation of SFEM can be obtained. Finally, several numerical examples using the von Mises elastic-plastic material model demonstrate the proposed method has good accuracy and robustness.