In this work a numerical model was developed to optimize a kinematic Gamma Stirling engine. In this model thermal and mechanical losses are included to approximate experimental results. The influences of three operation parameters (filling pressure (3, 5, 10 bar), hot end temperature (300, 400, 500 degrees C) and rotation speed (160, 360, 600 rpm)) as well as heat exchangers efficiencies on the Stirling engine performances are studied. The studied parameters are dependent and their interactions are significant for the Stirling engine brake power. For high initial filling pressure, the brake power became more sensitive to the rotation speed and the hot end temperature. The set of operation parameters giving the optimal brake power will be presented and discussed. It was found that the performances of the engine are more sensitive to its regenerator efficiency. For epsilon(r) = 0.5 the output brake power and the Carnot efficiency were dropped respectively of 16% and 5% relatively to epsilon(r) = 1. (C) 2015 Elsevier Ltd. All rights reserved.