Stirling engines represent a category of external heat transfer engines that demonstrate versatility by harnessing various heat sources, including solar energy, bio-mass, conventional fuel, and nuclear power. Achieving high thermal efficiency in power production has been a paramount concern driving researchers across the globe to focus on developing Stirling engines. In this particular research endeavor, a gamma type double-piston Stirling engine has been carefully selected for detailed analysis. To gain deeper insights into the engine's behavior, a polytropic model is employed in the investigation. The outcomes derived from the polytropic analysis are subsequently compared with classical adiabatic analysis. Remarkably, the polytropic approach significantly outperforms the classical adiabatic analysis in enhancing the overall performance of the Stirling engine. The results holds significant promise for advancing the efficiency and practical application of Stirling engines, reinforcing their position as a prominent contender in the pursuit of sustainable and highly efficient power generation technologies.