This paper deals with the lateral stability for a railway vehicle. Particularly, nonlinear critical speed is investigated via bifurcation analysis. Shooting method and trust region algorithm are applied to calculate the limit cycle of the nonlinear dynamic vehicle model. In case of the investigated vehicle model, the influences of the suspension parameters on the critical speeds are not large. The effects of friction coefficient are also small. However, there is an overall consistency that the nonlinear critical speed is decreased when the stiffness of the suspension is reduced. Study of the excitation conditions where the stable limit cycles occur gives very useful information to understand the nonlinear dynamic behavior of a railway vehicle and to test the vehicle with roller rig test stands. According to the results, the direction of the excitation is very important as well as the amplitude and frequency to acquire accurate nonlinear critical speed.