It is commonly accepted that the principal functions of an automobile suspension are to control low frequency rigid body motions, provide comfort to passengers, and to reduce tire normal force variation so that predictable handling is maintained. A good argument for reducing normal force variation is that in the extreme, if a tire is off the ground, it for certain cannot generate any lateral forces, and thus compromises lateral dynamics. The direct relationship between road holding and dynamic tire normal force variation is quantified sparsely in the literature.In this paper a relatively simple model is proposed which exposes how normal force variation at the front and rear directly affects the vehicle yaw rate and lateral acceleration. It is shown that normal force variation at the front has potentially the same effect on lateral dynamics as does the steering input.By proposing a 1/4 car vertical dynamic model, the tire normal force variation at the front and rear can be related to roadway unevenness. By combining the vertical and horizontal dynamic models, the lateral dynamics can be directly related to roadway unevenness. The results clearly demonstrate the effect of roadway unevenness on the lateral acceleration and yaw rate of automobiles. The model can also be used to develop control strategies to minimize tire normal force variation.