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Stirling cryocoolers with a single stage of expansion routinely achieve cryogenic refrigeration temperatures of 70 K. Lower temperatures can be achieved with multiple expansion stages arranged ‘in series’, 20 K with two stages, and less than 10 K with three or four stages. Multiple expansion Stirling power systems are also in prospect particularly for exhaust heat recovery systems using different stages of progressively lower temperatures. Two or more stages can be combined in a single cylinder. Multiple expansion Stirling machines have been a topic of interest at The University of Calgary for some years. Recently a second-order computer simulation program with integral graphics package for Stirling cryocoolers with up to four stages of expansion were developed and made available to the Stirling community. Adaptation of the program to multiple expansion Stirling power systems is anticipated. This paper briefly introduces the program and presents a specimen result.