A vehicle body, two bogie frames and two wheelsets for each bogie frame are used to describe the railway vehicle model. The system dynamic is modeled using a 38-DOF system including the longitudinal, lateral, vertical, roll, pitch and yaw displacements. A heuristic nonlinear creep model and the elastic rail are used to simulate the wheel-rail contact. Stable movement and the corresponding limit cycle motion are investigated. In order to study stability, bifurcation analyses are performed. These analyses are carried out for linear and nonlinear elastic rail model. It is revealed that the critical hunting speed evaluated via the nonlinear elastic rail is lower than that derived using a linear model.