The present invention concerns a fuel reservoir for a liquid fuel cell particularly useful for portable electronic devices in which the fuel reservoir can deliver the liquid fuel regardless of the orientation. The fuel reservoir comprises (a) a container defining a cavity for holding the liquid fuel; (b) a wicking structure positioned within the cavity and into which at least a portion of the liquid fuel wicks and from which said liquid fuel subsequently may be discharged or delivered, such as by pumping or wicking. The wicking structure is formed from a wicking material with a free rise wick height greater than at least one half of the longest dimension of the wicking structure. Among materials with such wicking capability are foams, matted, bundled or woven fibers and nonwoven fibers. The container may have a generally flat and thin profile, formed as a pouch or envelope with substantially planar top and bottom faces of flexible film material, such that the container holding the wicking structure and filled with the liquid fuel can be bent or shaped.