Abstract: In this paper,response surface methodology(RSM)is applied to study the relationship between structural parameters of free piston Stirling engine(FPSE)and responses.Theses parameters include the diameter of displacer's rod,the length of a heater,a regenerator and a cooler,and the output power and thermal efficiency are selected as responses.A regression model was presented to predict the performance of FPSE with different structural parameters.The analysis of variance(ANOVA)was conducted to describe the rationality of regression model and examine the statistical significance of factors.In addition,the influence of geometric parameters on output power and thermal efficiency were illustrated in 2D contour plot and 3D response surface.The results showed that the output power decreased with the parameters.While a larger length of heater and regenerator resulted in the increase of the thermal efficiency.The thermal efficiency could be optimal if a suitable length of cooler was chosen.Therefore,it is necessary to consider the influence of various factors on FPSE's performance to select the appropriate parameters.