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Ride is considered to be one of the criteria for evaluating the performance of a vehicle. However, the evaluation of ride quality of a car varies from person to person. There are many mathematical models which are used to study vehicle ride dynamics. The development of electronics, sensors and actuators has enabled the use of control systems to enhance the ride quality of a vehicle. This work deals with some of the commonly used ride models viz. Quarter Car model, 2 Degree of Freedom (DoF) Half Car Model and 4 DoF Half Car Model. A complete analysis of these models from a designer's perspective, e.g., variation of suspension stiffness, damping coefficient etc. is being presented. The response of these models to random excitation is being studied. The above mentioned models are based on the rigid body assumption. They do not incorporate a tire model which takes into account the stiffness and damping properties of the tire.