A mathematical simulation of an experimental regenerator has been developed that accounts for heat storage and heat loss from the peripheral pipework and from the regenerator walls as well. The simulation clearly substantiates the experimental results obtained for the regenerator section. In addition to the common dimensionless parameters, the regenerator performance also depends on the inlet fluid temperature variations, the heat capacity of the regenerator wads, the insulation, and the surrounding ambient temperature. The simulation results have revealed an important phenomenon: The average thermal effectiveness of a particular experimental investigation is constant regardless of the magnitude of the ambient temperature. This investigation provides an explanation as to why the experimentally measured values of the thermal effectiveness of the hot and cold strokes differ. Theory predicts that they should be equal at cyclic equilibrium. The simulation clearly shows that the use of internal and external insulations on the regenerator walls greatly reduces the difference in the effectiveness values.