The indicated power and thermal efficiency are the most important features of the Stirling engine. In the most general way, the efficiency depends on a set of parameters, such as the ratio between the volumes and temperatures of the working gas in the hot and cold compartment, the adiabatic function and energy losses due to friction processes between engine components. Stirling engines can use mono, bi or polyatomic molecules such as helium, hydrogen or carbon dioxide as working gases. The first part of the contribution is dedicated verification and completion of our results obtained on the basis of the technical design data of the Genoa03 Stirling engine. These were determined based on an analytical model of the thermal efficiency of a simplified thermodynamic cycle described in the pressure-volume diagram by two adiabatic transformations and two isochoric transformations. The input data used are those used by our αSETS calculation code. The second part of the article is dedicated to the analytical elaboration of the adiabatic function of the working gas for the case of a mixture consisting of two or three types of working gases at different molar ratios. The adiabatic functions are used to estimate thermal efficiency. It has been shown that a mixture of two or three types of gas does not improve the thermal efficiency of the Stirling engine compared to the use of one-component gas. The results of these models related to the Beale relationship can be used successfully in the design process of Stirling engines