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Appraisal of contact stresses, surface cracks, and plastic deformations in rails and wheels has always been an important issue in mechanical and railway engineering because of two main reasons. In the first place, these inappropriate events lead to the reduction of service life of the railway track. Besides, studying railway systems requires both time-consuming analysis methods and expensive experimental works. In this paper, a railway system containing wheel, rail, axle, and pads is modeled and analyzed. Using elastic-plastic materials, mapped meshing, and the rolling motion of the wheel contingent upon the up-to-date international railway systems results in high accuracy in the solutions of this problem. ANSYS software is utilized with the purpose of simulating the system. The contribution of this study is on the basic way of managing Rail-Wheel interaction problems from a finite element method point of view. So, stress distribution, elastic and plastic strains as well as nodal forces are considered, simultaneously. The results obtained from the simulation have suitable agreement with the real life experiences. Another feature of this paper is that it demonstrates essential steps for more realistic 3D solutions to the aforementioned problems.