Dampers provide safety by controlling unwanted motion that is caused due to the conversion of mechanical work into another form of energy (e.g., heat). State-of-the-art materials are elastomers and include thermoplastic elastomers. For the polymer-appropriate replacement of multi-component shock absorbers comprising mounts, rods, hydraulic fluids, pneumatic devices, or electro-magnetic devices, among others, in-depth insights into the mechanical characteristics of damper materials are required. 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. The results revealed that the material parameter determination methodology is reliable, and the data that were applied for simulation led to realistic predictions. Interestingly, the rebound resilience of the mixture of soft and hard PDMS (50:50) wt% was the highest, and the lowest values were measured for TPU.