In order to avoid unpleasant incidents, it is crucial to maintain the stability for a high-speed railway vehicle. In this research, a high-speed railway vehicle dynamics with 38 degrees of freedom was investigated, adding longitudinal movement equations. Another innovation of this investigation is to determine the critical velocity for the studied railway vehicle and using nonlinear elastic rail for the wheel and rail contact. In this study, the stable and hunting behavior of the system was investigated. To identify the chaotic motion of the system, frequency analysis has been performed. Also, by plotting the Poincaré map, dynamic behavior of the system is illustrated in a discrete state space, which could be a good criteria for the chaotic or periodic behavior of the system. Long-term behavior reveals that at Speeds lower than the critical speed, the system oscillates until it reaches the steady-state of the system. In steady motion, the oscillation continues until the critical speed When the system reaches the critical velocity, the motion on the limit cycle occurs for the first time and when the speed is higher than critical speed, the vibration amplitude increased smoothly. It was observed from the frequency response plot that the hunting frequency evaluated via the linear elastic rail is higher than that of derived using a nonlinear model.