In this paper, an irreversible thermodynamic cycle working between two constant temperature external reservoirs is proposed to model the practical Stirling engine by applying finite time thermodynamics (FIT). To analyze the regenerative processes, the regenerator is assumed to consist of numerous smaller heat reservoirs with individual temperature, and the irreversible heat transfer occurs between the working fluid and these smaller heat reservoirs. To analyze the expansive and compressive processes, polytropic processes are adopted to model the expansive and compressive processes, and corresponding polytropic exponents are obtained by thermodynamics for the first time. Based on the proposed thermodynamic model, the expression of thermal efficiency and output power are derived. In addition, the effects of thermodynamic parameters on power and efficiency are investigated to evaluate the performance of the proposed model. To optimize the proposed Stirling cycle model, an intelligent optimization algorithm named multi-objective particle swarm optimization based on crowding distance (MOPSOCD) is adopted to optimize the output power and thermal efficiency simultaneously. (C) 2019 Elsevier Ltd. All rights reserved.