This paper describes our three simulation models for Stirling (ST) and Vuilleumier (VM) cycle machines and the findings obtained from numerical analysis. The first is the simulation model for the ST machine based on 3rd-order method which is used to make clear the working gas behavior and to predict and evaluate the performance of the ST machine. The second is the 3rd-order model for the VM machine. The third is the isothermal model to clarify the relationship between the ST and VM machines. These models have been applied to the researchand development of a 4 cylinder double-acting type ST engine (NS30S) and a VM cycle heat pump system (DDHP).