The contrast between travel convenience and ride quality for production of suspension systems always existed with consideration of stability in changing the line or crossing the barriers. In addition, by increasing each parameter, the other one decreased. With advancement in control systems, the suspension systems are gradually changed and semi-active and active suspension systems have entered the markets. Using advance sensors lead to decrease the design problems until the scanners decreased the available contrast completely. Later, the electromagnetic active suspension systems created two criteria include stability and travel convenience, simultaneously. This type of suspension came while the progress of the Boos company vehicles were employed And vast difference compared to the passive suspension vehicles were seen The new generation of vehicles using electromagnetic active suspension system . To equip this type of suspension on the car, there was a problem and the high cost of this type of suspension was that led to this type of suspension is for to luxury cars. In this thesis, for the first time, an eight degree-of-freedom car model with the objective function including travel convenience and constraints relating to the design of suspension system thus driver convenience is optimized in Adams software in order to obtain the initial values for commencement of simulation along with the validity of active and inactive suspension systems. It causes that valuable comparative method is theorical that have been optimized for superior passive mode to active mode denies knowing this of design Constraint in optimizaition process used for a suspension systems and then the comfort and ride quality criteria. These criteria were considered in the optimization process. Also, for this project using eight degree-of-freedom car model is used for two conditions. Attempts tended to investigate the small stability of a car. In addition, the distinction of active suspension in different path includes longitudinal and latitudinal slope in direct straight road and in curv road with constant radius for constant and variable speed compare to passive suspension is validated. The reduction of bumpiness and change in direction with the advantages of active suspension systems is studied such that each of the variables to be in the sutible range of stability. Using this method, the possibility of computing the maximum speed for moving in curv road is obtained. Finally, the time required for the function of active suspension in order to perform is calculated. Keywords Active suspension system, Ride quality, Eight degree of freedom model, Optimization, Small stability, lateral steepness, Stability of large deviation, Urung mass.