Dampers provide safety by control of unwanted motion, due to conversion of mechanical work into another form of energy (e.g., heat). State of the art materials are elastomers including thermoplastic-elastomers. For polymer-appropriate replacement of multi-component shock absorbers comprising mounts, rods, hydraulic fluids, pneumatic devices, or electro-magnetic devices, among others, deep insights of the dynamic thermo-mechanical characteristics of damper materials have to be gained. The ultimate objective is to reduce complexity by utilizing inherent material damping rather than structural (multi-component) damping properties. The objective of this work was to compare the damping behavior of different elastomeric materials including thermoplastic poly(urethane) (TPU), and silicone rubber blends (mixtures of different poly(dimethylsiloxane) (PDMS)). Therefore, the materials were hyper- and viscoelastic characterized, a finite element calculation of a ball-drop test was performed, and for validation the rebound resilience was measured experimentally. In an attempt, the coil-over shock absorber of a model car was replaced by a damper made of the examined and modeled materials. The results revealed that the material parameter determination methodology is reliable, and the data applied for simulation lead to realistic predictions. Interestingly, the rebound resilience of the mixture of soft and hard PDMS (50:50)w% is the highest and the lowest values were measured for TPU.