The lateral Motion of the vehicle is studied under the situations of steering, where the yaw control of the vehicle is focused on the stability of the vehicle under extreme steering conditions. In this paper, bicycle models for low-speed and high-speed operation are presented with emphasis on the kinematic model at low-speed operation and the dynamic model at high-speed operation. A state space model is developed with 2 dof and state space variables are presented for calculating slip angle and yaw angle. The parametric variation of slip angle and yaw angle is tabulated for various steering angles within the range of 110 to 28.560. A Python code was developed and simulated for under-steer and over-steer conditions depending on the corner stiffness of the front and rear wheels. The results were presented for further improvement of the model analysis with road banking angle and total vehicle model.