AbstractThe paper presents mathematical models which have been developed by the authors, and the results of which may be used to design an experimental refrigeration unit operating in the Stirling cycle. The systems engineered and based on Stirling cycle may be considered as an alternative to commonly employed internal combustion engines and Linde circulation cooling systems. The article presents a time discretization model assuming the cylinders as adiabatic spaces. The model enables the size optimization of all particular elements of the Stirling device such as: heat exchangers, the regenerator, the cylinders, piston motion and phase displacement. The advantage of modelling is the calculation speed when compared to modelling based on full Navier-Stokes system of equations (CFD) therefore enabling the dimensioning of the device. The results obtained using the simplified model have been verified by the other modelling type – that is the full 3D CFD, in which the whole working space including the heat exchangers and the regenerator has been modelled. Additionally, a dynamic MESH option has been applied in order to simulate the movement of the pistons in the cylinders.