A theoretical study on the vibration isolation and energy absorption capability of high porosity closed-cell aluminum foams subjected to impact loading is presented. A double degree of freedom (DDF) spring-damper-foam collision model (mimicking important equipment and/or personnel) is established to explore the physical mechanisms of shock attenuation when the system as a whole is dropped from a given height and collides with hard ground. For validation, the finite element method is employed to simulate directly the dynamic responses of the whole system. The effects of key system parameters including spring stiffness, damping ratio, mass ratio, initial impact velocity and foam thickness on the mass of the foam cushion and peak acceleration of the protected structure are quantified. The DDF model is subsequently employed to minimize the weight of the foam cushion against impact energy subjected to different design constraints; the corresponding optimal geometrical dimensions of the foam cushion are also obtained.