The Stirling machine has many successful applications mainly thanks to its high efficiency, fast cool-down, small size, light weight, low power consumption and high reliability (heating and cooling). A Beta type Stirling refrigerator is studied experimentally and numerically. The mathematical model takes into account complex phenomena related to compressible fluid mechanics, thermodynamics and heat transfer losses. A special attention is paid to the effect of geometric parameters such as dead and swept volumes respectively in compression and expansion spaces. Regenerator length, diameter and porosity are also discussed and optimal parameters are proposed. The effect of speed on the cold end temperature and refrigerator's performances is also investigated. Net cooling capacity, input power and COP were estimated at different conditions. Results allow understanding the physical processes occurring in the refrigerator and for predicting its performance.