The only substantial source of vibration and noise is the IC engine itself. Vibration causes system failures or damage, which is bad for the supporting system for the engine. It is necessary to ensure correct mounting in order to prevent engine vibration. Engine Mounting is one of the basic but important design characteristics in a vehicle. The engine mounts are designed with optimum stiffness and damping so as to reduce the system vibration and avoid resonance phenomenon. This paper deals with the two characteristics namely damping coefficient and stiffness of the Anti-Vibration Mounts. The modal analysis and Harmonic analysis of different models of AVM has been performed. From the dynamic analysis the optimized characteristics of AVM are obtained. The model is optimized for minimum acceleration by varying two factors, i.e. stiffness and damping coefficient of AVM. Taguchi method has been used for optimization Vibration response of system using a commercial Minitab software. It is observed that the optimize values of stiffness is 450 N/mm and damping coefficient is 0.03 NS/mm. From Numerical Analysis, it is observed that the vibration response amplitude is decreases by 13.91% by using optimized AVM.