A mathematical model for the calculation of the Stirling cycle and of similar processes is presented. The model comprises a method to reproduce schematically any kind of process configuration, including free piston engines. The differential balance equations describing the process are solved by a stable integration algorithm. Heat transfer and pressure loss are calculated by using new correlations, which consider the special conditions of the periodic compression/expansion respectively of the oscillating flow. A comparison between experimental data achieved by means of a test apparatus and calculated data shows a good agreement.