Ratcheting is a cyclic accumulation of strain under a cyclic loading. It is a kind of mechanisms which generate cracks in rail steels. Though some experimental and numerical study has been performed, modeling of ratcheting is still a challenging problem. In this study, an elastic-plastic constitutive equation with non-linear kinematic hardening equation was applied. Contact stresses in wheel-rail were analyzed. Under the tangential stress of the contact stresses, a cyclic stress-strain relation was obtained by using the model. A constant ratcheting strain per cycle was accumulated.