This report was prepared in support of the Renewable Energy Applications and Training Project that is sponsored by the U.S. Agency for International Development for which ORNL provides technical assistance. It briefly outlines the performance that might be achievable from various kinds of Stirling-engine-driven irrigation pumps. Some emphasis is placed on the very simple liquid-piston engines that have been the subject of research in recent years and are suitable for manufacture in less well-developed countries. In addition to the results quoted here (possible limits on M4 and pumping head for different-size engines and various operating conditions), the method of calculation is described in sufficient detail for engineers to apply the techniques to other Stirling engine designs for comparison.