Exploring the mechanical properties of soft tissues under compressive loading is crucial for understanding their role in automobile incidents. Soft tissues, which serve as cushions or padding between bone and vehicle interiors, significantly influence contact duration and forces, thereby altering incident kinematics and injury risk assessment. In this investigation, muscle and soft connective tissues from post-mortem human subjects (PMHS) forearms were excised and subjected to compression and indentation testing methods at various rates and strains. Anthropomorphic Test Devices (ATDs) upper extremity foam and vinyl foam composite material surrogate tissues underwent similar testing for comparison. High impact rates simulating those in high-speed car collisions were achieved using a custom-built drop tower. The results revealed substantial differences in stiffness between soft tissues and ATD materials across most loading rates and strains, although some exceptions were noted at higher rates and strains. Indentation and modified Zener models were used to quantify material parameters. The indentation model could characterize human muscle, soft connective tissues and ATD vinyl foam composites, but fell short with ATD foam materials. The Zener model effectively derived material parameters for the tested human tissues but encountered difficulties characterizing both ATD materials. This highlights the need for further refinement to develop a constitutive model for both materials. These findings provide a solid basis for advancing ATD surrogate materials and have broader implications for soft tissue research. Moreover, this work represents a crucial step towards enhancing safety standards in the automotive industry.