The four processes of a reverse Stirling heat pump cycle; isothehermal compression with the heat of compression being transmitted to a constant, relatively high temperature sink, regenerative cooling, isothermal expansion with heat flow from a cooler, constant temperature source followed by regenerative heating from the heat derived from the previously compressed gas are all performed with constant rather than intermittent flow. A constant flow, constant volume counter-flow heat exchanger, placed between the compressor and expander, rather than an alternately heated and cooled heat storage matrix, provides for the steady flow regenerative heat transfer as required for a steady reverse Stirling cycle heat pump. This invention therefore provides for increased heat pump rate per unit volume.