In 2004, the author of this thesis invented a novel metal-diaphragm based pressure wave generator (DPWG) for pulse tube and Stirling cryocoolers. The invention used a connected pair of metal diaphragms to seal the cryocooler’s clean working gas from a conventionally lubricated drive mechanism at ambient pressure, and to balance the average gas forces on the working diaphragms so the drive only has to work against the pressure wave. The DPWG has since been developed and has proven to be effective and practical, driving pulse tube cryocoolers with up to 1200 W of refrigeration at 77 K. From early in the development of the DPWG, two questions have existed. The first is: Can the connected pair of diaphragms concept suspend the displacer in a free-piston Stirling cryocooler, removing displacer piston-to-cylinder sealing issues? And the second is: Can the large surface areas and radial flows offered by the diaphragms’ flat geometry be used for heat exchange, thus reducing the need for costly heat exchangers? This thesis addresses those two questions. To address the first question, a proof-of-concept prototype was designed, constructed and tested. It did not perform as well as expected but did reach cryogenic temperatures. A second prototype with smaller displacer diaphragms was then designed and constructed. Its performance was significantly better than the first prototype; it achieved a low temperature of 56 K and produced 29 W of refrigeration at 77 K. The prototypes proved that the double diaphragm concept could be used to produce a free-piston Stirling cryocooler and perform refrigeration at cryogenic temperatures. To address the second question, two computer models of the second prototype were developed. The first was with a one-dimensional Stirling machine modeller called Sage; the second with ANSYS® CFX, a commercial Computational Fluid Dynamics (CFD) code. A series of validation exercises were performed to confirm the models’ applicability to the oscillating flow and heat transfer typical of Stirling cryocooler gas spaces. The second prototype was modelled using Sage and CFX; both agreed with the macroscopic behaviour of the prototype and predicted the cooling power within an order of magnitude of the experiments. The CFD model confirmed the second question for the diaphragm on the cold side of the displacer, which was sufficient for heat exchange without a separate heat exchanger. However, it showed that the warm side of the machine needed extra area for heat rejection. The CFD model gave insights into why the second prototype was not performing as well as intended. A CFD model of a modified design, backed up with a Sage model, has predicted that it is possible to make a cryocooler with performance similar to a pulse tube with the same size pressure wave generator and with a higher efficiency.