This paper describes a new mathematical model developed to account for nonlinearities between vehicles and tires. Lateral and vertical stiffnesses of tires are investigated because they have basic influences on the behavior of the car in sudden and severe maneuvers. The new procedure allows operational simulation and simplifies analyses of cars with different types of tires and suspensions. This is demonstrated by comparing vehicles fitted with a basic tire, a tire with larger lateral stiffness, and a tire with larger cornering stiffness. Calculations show the damping effect of lateral stiffness and the need for increasing both cornering and lateral stiffnesses.