A method and apparatus for separation of H.sub.2 gas from a gaseous mixture utilizing an H.sub.2 gas permeable metallic membrane supported directly on a porous substrate made up of at least one porous polymeric hollow fiber. In accordance with one preferred embodiment, the porous substrate is made up of a plurality of porous polymeric hollow fibers, forming a porous hollow fiber membrane. In accordance with one embodiment, a cooling fluid is disposed in contact with the hollow fiber, thereby enabling advantageous operation of the H.sub.2 gas separation process at elevated temperatures in the range of about 200.degree. F. to about 800.degree. F.