The problem related to the rotational vibration at steering wheel end of passenger cars during high speed driving is investigated. to analyze vibration of steering wheel, a steering system of passenger car is modelled in twelve degrees of freedom including backlash effect of rack and pinion gear system. The one degree of freedom system with backlash in investigated by the analytical method. Consequently the skeleton curve and the frequency response curves are computed. The steering system is analyzed by the numerical simulation using the 4th order Runge-Kutta method, the obtained results are compared with the experimental data. Also the effects of the change of rack gear tooth stiffness and backlash on the acceleration level of steering wheel are investigated. As a result, it can be found that the acceleration level of steering wheel becames lower as the rack gear tooth stiffness becames higher, and that acceleration level becames high as the magnitude of backlash between rack and pinion gear increase.