In this paper, characteristic analysis of vehicle's lateral dynamics is proposed to understand the nonlinear behavior of vehicle system. It was observed in Liaw and Chung (2006) that, with the variation of the front wheel steering angle, the vehicle dynamics would exhibit the saddle-node bifurcation. That might result in spin motion and/or system instability. To find out the key factors for causing the instability of vehicle system, the driving speed, the vehicle's mass and the location of the center of gravity were treated as system variables for analytical study. Numerical simulations for an example model demonstrate the main results of the theoretical analysis.