With the development of the train’s speed, the lateral stability of high speed passenger car is the research focus in recent years. A mathematical model of half railway vehicle model is established with 9 degree freedom. Numerical method is used to study the system’s lateral stability and bifurcation problems, the critical speed and transition process of motion state are obtained. The results indicate that some complex dynamical behavior included simple periodic, two periodic, chaotic motion and so on are existed, and it changes from symmetric to asymmetric, finally changes into symmetric motion, which are found beyond critical speed.