A sinusoidal model is proposed to analyze the thermodynamic processes of gas parcels oscillating in a regenerator. The regenerator is considered equivalent to a bundle of capillary tubes with large thermal capacities. With perfect thermal contact between the gas and tube wall and the proper phase shift between velocity and pressure, the overall effect of a gas parcel oscillating in the capillary in one cycle is that it absorbs heat from one lengthwise part of the wall and delivers heat to the other part of the wall within its range of displacement. Each gas parcel working in the regenerator undergoes a thermodynamic cycle. When the work flow is in the same direction as the temperature gradient of the regenerator, it undergoes a heat engine cycle. Otherwise it undergoes a refrigeration cycle. The regenerator can work as a heat engine or as a refrigerator. ©1997 American Institute of Physics.