A technique for calculating the efficiency and power of Stirling machines is presented. This technique is based on the First Law of Thermodynamics for processes with Finite speed and the Direct Method for closed systems, In order to apply the Direct Method to Stirling Cycles, a new and novel PV Px diagram is presented that shows the effects of pressure losses due to friction, finite speed and throttling processes in the regenerator of the Stirling engine. The method used for the analysis of this irreversible cycle with finite speed involves the direct integration of equations based on the first law for processed, with finite speed to obtain the cycle efficiency and power directly, This technique is termed the Direct Method. The results predicted by this analysis are in good agreement with the actual engine performance data of 12 different Stirling engines, over a range Of Output from economy to maximum power. This provides a solid verification that this analysis. based on the Direct Method, can accurately predict actual Stirling engine performance. particularly with regard to efficiency and output power. In addition to the powerful predictive capabilities of the Direct Method. the new PV Px diagram for the Stirling cycle is both an effective and an intuitive tool for explaining the operation and design of Stirling machines. Copyright (C), 2002 John Wiley Sons. Ltd.