In order to study further the promising free piston Stirling engine architecture, there is a need of an analytical thermodynamic model which could be used in a dynamical analysis for preliminary design. To aim at more realistic values, the models have to take into account the heat losses and irreversibilities on the engine. An analytical model which encompasses the critical flaws of the regenerator and furthermore the heat exchangers effectivenesses has been developed. This model has been validated using the whole range of the experimental data available from the General Motor GPU-3 Stirling engine prototype. The effects of the technological and operating parameters on Stirling engine performance have been investigated. In addition to the regenerator influence, the effect of the cooler effectiveness is underlined.