The aim of this paper is to provide a multi-objective model to evaluate the effect of engine working parameters on the performance characteristics of a beta-type Stirling engine. The second objective of the study is to enhance the specific power of the engine, which was designed and manufactured in a previous study, via increasing the compression ratio. The selected independent variables were: charge pressure (2-9 bar), heating temperature (500-700 degrees C), and engine speed (550-750 rpm). The engine was analysed using the design of experiments based on the response surface method, and the most appropriate model was achieved. The desirability function approach was used to determine the optimum engine working condition. Optimal engine speed, charge pressure, charge pressure were 700 rpm, 8 bar, and 700 degrees C, respectively, with the desirability value of 0.86. At optimal engine working conditions, the amounts of the brake torque and brake power were found to be 11.95 Nm and 868.13 W, respectively. Optimized parameters are then compared and validated against the experimental data of the Stirling engine with an error of 4%. The specific power of the engine was found to be 1100 W/L which is 13% higher than the previous design. (C) 2020 Elsevier Ltd. All rights reserved.