In this study, response surface methodology (RSM) and the desirability approach are applied to study and optimize the performance of a free piston Stirling engine (FPSE). A regression model is presented to investigate the influences of operating and structural parameters of the FPSE on its performance. The analysis of variance (ANOVA) is conducted to describe the rationality of the regression model and examine the statistical significance of factors. Also, the relationship between output power, thermal and exergy efficiency and these parameters of Stirling engine is presented via 2D contour and 3D surface plots. Moreover, the operating and structural parameters of FPSE are optimized to achieve maximal output power, thermal and exergy efficiencies simultaneously. The multi-objective optimal results are confirmed by Sage software simulation results. It is found that the errors between the Sage modeling and RSM values for output power, thermal and exergy efficiency are 0.37%, 1.51% and 1.40%, respectively. Therefore, the model based on the RSM method is an efficient and fast way for the design and optimization of the FPSEs.