Onboard hydrogen storage technology is critical component in the realization of a hydrogen-powered economy. Currently, there are four technologies suitable for vehicular hydrogen storage: compressed gas, metal hydride materials, carbon-based materials, and cryogenic liquid. In this study, finite element models of a spherical, double bubble, and truncated octahedron cryogenic capable pressure vessel were created and subjected to internal pressures ranging from 2500 psi to 10,000 psi and temperatures ranging from 20.28 K TO 300 K. Each vessel was modeled with a carbon fiber/epoxy laminate wrapped around its outer shell. From the stress and thermal analyses, it was determined that the spherical vessel experienced the least stress amongst the vessels and that the usage of a carbon fiber/epoxy laminate results in ~20% reduction in the stress experienced by the vessel. It predicted that both the spherical and the double bubble vessel designs would be suitable for the storage of liquid hydrogen at cryogenic temperatures and high pressure. Based off of the results of the analyses, it was deemed feasible to create a modular cubic cryogenic capable pressure vessel with a spherical inner vessel and a cubic vacuum outer jacket.