Automotive Frontal bumper systems address two goals. First, is to lessen the inward intrusion during crash scenario and the second is to guarantee pedestrian safety. A good bumper design would try to fulfill these two goals while maintaining its weight as low as feasible to improve energy consumption. In this paper, we try to add to these two functions, a new condition, that is the ability to maintain the minimum possible lasting plastic damage during low speed crashes. This would develop both the crashworthiness of the bumper and the pedestrian safety. We address this condition by assuring that the bumper deformations stay close to the elastic zone of the material. Due to the limited range of the material elastic deformations of the bumper, even at low speeds, we try to complement it with a visco-elastic process. This is achieved by alternating the brackets connecting the bumper to the car structure elements with a spring-dashpot system that provides the desired visco-elastic response, allowing the bumper beam to deform nearly elastically. Finite element analysis is used in the study of the spring-dashpot system parameters to reach the optimum configuration that ensure minimization of plastic deformations in the bumper structure at low speeds of 5 miles/hour crash. The consequence of varying the thickness of the bumper beam is also investigated in this regard. A basic parameterized finite element model of the Ford Crown Victoria bumper form is used in several crash simulations carried out with the explicit dynamics system LS-DYNA3D to test the validity of this bumper system.