An inertance tube pulse tube refrigerator with a step piston compressor is a reversible refrigerator which means that it can be operated as a refrigerator, a cold engine, a heat engine, and a heat pump. We call it as a pulse tube machine. In this paper, a numerical simulation is conducted on an inertance tube pulse tube machine with a step piston compressor. The result shows that the pulse tube machine can work as a refrigerator, a cold engine, a heat engine, and a heat pump, depending on the swept volume ratio of the step piston compressor. (c) 2016 Elsevier Ltd. All rights reserved.