An evaluation of the major theoretical considerations concerning the design of an endoreversible Stirling cycle with ideal regeneration is given. The factors affecting optimum power and efficiency at optimum power are analysed for the cycle based upon higher and lower temperature bounds. Heat transfer characteristics of the regenerator and the thermal source and sink, individual process times for the cycle have been studied with respect to engine design parameters like speed, compression ratio, etc. The results of this study provide additional information for use in the optimized design and evaluation of Stirling engines.