A system and method of producing hydrogen from a mixture of hydrocarbon fuel and steam. Reaction cells are provided that each contains a first tube of hydrogen permeable material and a second tube of hydrogen impermeable material that are concentrically positioned. This creates a gap space between the first tube and the second tube. The gap space is heated by burning a combustion gas outside of the two concentric tubes. A water gas shift reaction occurs in the gap space. Hydrogen is created that permeates through the first tube and becomes separated from the remainder of the reaction gases. The hydrogen gas is collected for use. As such, the system and method acts both as a gas shift reactor and as a hydrogen separator even though it is a single unit.