This paper presents a detailed investigation of vehicle ride response using a semiactive suspension with a shock absorber of dual damping characteristics. For the purpose of vehicle ride analysis, different mathematical models have been developed with different levels of complexity. Numerical simulation has been carried out through the MATLAB/Simulink environment and aids the future development of controllable suspension systems to improve the vehicle‟s ride comfort. A detailed parametric study has been introduced to investigate the effect of suspension system parameters on the ride comfort. The findings conform to natural intuition and well known published research.