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Using the finite element code ANSYS/LS-DYNA, a dynamic finite element model with an elastic-linear-kinematic-hardening plastic material is established to analyze elastic-plastic stresses in the railhead in the impact process of wheel and rail occurring at the gap of rail joint. The model is based on the discrete elastic support condition of the rails, which is suitable for the actual situation of wheeL/track rolling contact. In the analysis the influences of axle load, yield stress and tangent modulus of rail material on the stresses and strains are investigated in detail. The distribution of stresses and strains in the jointed railhead are given. It is found that the axle load, yield stress and tangent modulus of rail material greatly affect the stresses and strains in the railhead during impacting. The study provides a reliable method and useful datum for the further research on fatigue and wear of railhead and improving the rail joint mode.