Abstract: The dynamic behavior of a wheel rail system was investigated. Melan's (lower bound) shakedown theorem was examined and applied to calculate the shakedown limits. The preliminary research results indicate that the short wavelength corrugation of the rail is due to a large amount of energy from the vibration components at high frequency. The finite element analysis of the wheel rail contact shows that the maximum stress under the subsurface exceeds first yield strength, which leads to plastic deformation.