Mechanical impact events such as vehicle collisions, ballistic loads, and blast waves can adversely affect both civilians and military personnel. Engineered polymers can be optimized as protective materials that minimize organ injury by dissipating mechanical energy, or as synthetic simulants of biological soft tissue’s impact response. To improve survivability, it is critical to understand and control the energy dissipation mechanisms of “soft matter” under extreme impact loading conditions. Here, we synthesized, characterized quantitatively, and modeled computationally the mechanical deformation of novel polymeric gels from the molecular to macroscale. Our engineered polydimethylsiloxane (PDMS) gels exhibit structural features on multiple length scales and mechanical responses on multiple timescales, enabling us to precisely tune the system to match the impact penetration depth and impact energy dissipation profile of cardiac muscle or brain tissue. Synthetic gels that accurately recapitulate the impact response of soft tissues allow for understanding injury mechanisms, predicting injury severity, and assessing new protective equipment.