A cell for use in a solid polymer electrolyte fuel cell, including a membrane electrode assembly including a fuel electrode and an oxidant electrode disposed on either side of a solid polymer electrolyte membrane, the assembly being sandwiched from either side by a first separator and a second separator to give a stacked construction. The first and second separator have a planar shape slightly larger than a solid polymer electrolyte membrane, with primary face seal rubber layers affixed to outer peripheral edge portions of primary faces of the first and second separator. Thus, an outer peripheral edge portion of the solid polymer electrolyte membrane projecting outwardly beyond the fuel and oxidant electrodes are held clamped fluid-tightly between the first and second separators by means of the primary face seal rubber layers of the first and second separators.