Abstract: A lightweight, cryogenic-compatible pressure vessel for flexibly storing cryogenic liquid fuels or compressed gas fuels at cryogenic or ambient temperatures. The pressure vessel has an inner pressure container enclosing a fuel storage volume, an outer container surrounding the inner pressure container to form an evacuated space therebetween, and a thermal insulator surrounding the inner pressure container in the evacuated space to inhibit heat transfer. Additionally, vacuum loss from fuel permeation is substantially inhibited in the evacuated space by, for example, lining the container liner with a layer of fuel-impermeable material, capturing the permeated fuel in the evacuated space, or purging the permeated fuel from the evacuated space.