A substantial program of research on miniature cryogenic cooling engines operating on the Stirling cycle is presently in progress. One part of this work involves the digital-computer simulation of the cycle which in turn requires accurate and detailed knowledge of the heat-transfer and friction characteristics of the matrix material used for the contraflow thermal regenerator of the Stirling cycle. It has been found by experience that the matrix material for Stirling-cycle regenerators must be more finely divided than the materials characteristically used for gas-turbine and air-preheater regenerative heat exchangers. This is because the porous volume of the Stirling-cycle regenerator constitutes a substantial part of the dead volume in the total working space of the machine, and any increase in the dead volume has a highly deleterious effect on machine performance because of the reduced pressure ratio. Very dense-mesh wire screen has proved to be a satisfactory material for the regenerators of small Stirling-cycle cryogenic cooling engines.