Polymeric materials have played a significant role in the adoption of a multi-materials approach towards the development of a safe and cost-effective solution for hydrogen fuel storage in Fuel Cell Vehicles (FCVs). Numerous studies exist with regards to the exposure of polymeric materials to gaseous hydrogen as applicable to the hydrogen infrastructure and related compression, storage, delivery, and dispensing operations of hydrogen at fueling stations. However, the behavior of these soft materials under high pressure hydrogen environments has not been well understood. This study involves exposure of select thermoplastic and elastomeric polymers to high pressure hydrogen (70-100 MPa) under static, isothermal, and isobaric conditions followed by characterization of physical properties and mechanical performance. Special attempt has been made to explain hydrogen effects on polymer properties in terms of polymer structure-property relationships, and also understand the influential role played by additives such as fillers, plasticizers, and processing aids in polymers exposed to hydrogen. Efforts have also been focused on deriving suitable conditions of static testing in high pressure hydrogen environments as a valuable part of developing a suitable test methodology for such systems. Understanding the relationships between polymer composition and microstructure, time of exposure, rate of depressurization, purge and exposure conditions, etc. in this simple study will help better define the test parameters for upcoming high pressure cycling experiments in hydrogen.