A cylindrical, annular axial flow heat exchanger for use as a gas cooler in a thermal regenerative machine such as a Stirling engine is provided. The heat exchanger includes an outer shell of sufficient strength and thickness to withstand the pressure exerted by the working fluid and a tubular member positioned adjacent to and in contact with the outer shell, the tubular member having spaced apart sidewalls defining a flow passage therebetween. At least one of the sidewalls of the tubular member is embossed with ribs, the ribs being in contact with the inner surface of the outer shell thereby defining axially extending flow passages between the outer shell and tubular member along the circumference thereof for the flow of a second, gaseous fluid through the heat exchanger. The first fluid flows circumferentially through tubular member, while the second fluid flows axially between the outer shell and the tubular member.