The lateral mathematical model of a high speed vehicle system with 17 degrees of freedom is set up and the nonlinearities arising duo to suspension parameters and wheel/rail interactions are considered. The coupler traction force in tension and compression cases which is the function of vehicle speed and position in the trainset is also taken into account in the model. The critical speed at the Hopf bifurcation point on straight and circular curved tracks are studied by utilizing efficient numerical methods. The influence of track curve radius and superelevation on the critical speed is investigated.