The Stirling engine performances depend on several physicals characteristics and functioning parameters. The influence of each parameter and of their interactions is difficult to achieve with classical univariate studies. The experimental design is an alternative to identify the parameters sets allowing optimal Stirling engine performances. Hence, a four factor Central Composite Rotatable Design was used to observe the effect of cooling water flowrate, initial charge pressure, heating temperature, and operation time on a Stirling engine brake power. The influence of each parameter and the effect of the interaction between two or three parameters on the engine performances are presented and discussed. Using the surface response method, it appears that initial charge pressure and heating temperature are the more influencing parameters on the Stirling engine performances. With modeling, optimal conditions for the Stirling engine functioning are the following: charge pressure of 8 bar, heating temperature of 500 °C, and cooling water flow rates of 7.34 l/min, independent of the engine operation time. Copyright © 2012 John Wiley & Sons, Ltd.