The further development of a model to accurately simulate the performance and detailed behavior of Stirling cycle machines is described. The transport equation set (which describe the working gas) is derived in both the so-called integral and differential forms. Only the integral equation set is solved for the simulation. The differential equation set is used to investigate the structure of individual terms in the integral equation set. This procedure allows these terms to be more accurately understood and, hence, modeled. The energy equation includes kinetic energy and dissipation terms while the momentum equation includes the effects of working gas acceleration and viscous friction. Heat leakage and longitudinal conduction in the machine walls are accounted for and due regard is taken of the working gas instantaneous properties. The Reynolds analogy is used to calculate the local heat transfer coefficients.