The Stirling engine, a type of external-combustion engine utilizing a compressible fluid as its working medium, holds promise as a highly efficient device for converting heat into mechanical work at Carnot efficiency. This research conducts a detailed analysis, comparing the Hargreaves isothermal model and the Schmidt model specifically for the gamma type Stirling engine. The study examines the impact of dead volume on the engine's performance, revealing that the engine network is solely influenced by these volumes. Furthermore, it highlights the effectiveness of Hargreaves model for the performance analysis of gamma type Stirling engines.