The damping of a shock absorption device composed of nonlinear disk spring stacks and rubber rings was investigated. Friction forces of rubber rings and hysteresis of disk springs were obtained experimentally. The hysteresis curves of several types of disk spring stacks were approximated, from which the energy dissipated was estimated. Based upon the friction force and the energy dissipated, 4 damping models were presented and shock responses of the damping models were investigated. The hysteresis of disk spring is more meaningful than the friction of the rubber ring for the damping. For practical use, equivalent viscous damping model for total energy dissipated per cycle was suggested.