Abstract: The Stirling engine is an externally heated combustion engine that uses gas as the working medium. It has the advantages of high thermal efficiency, low noise, and low pollution. To prevent the contamination of the gas medium, the engine uses an oil-free lubrication design. The PTFE-based piston rings operate under high temperatures, high pressure, and varying loads, making them prone to wear, which can reduce sealing performance, increase leakage, lower engine efficiency and shorten the engine’s lifespan, or even damage the entire engine. Therefore, improving the wear resistance of the piston rings in Stirlingr engines has become an urgent issue. Surface texturing, as an effective method to reduce friction and improve lubrication, has been widely used for tribo-pairs such as the internal combustion engines with oil lubrication. By conducting a comparative analysis of the load-carrying capacity of the dimple textures under gas and liquid lubrication conditions, this study aims to explore the differences between gas lubrication and liquid lubrication, summarize design guidelines for texture parameters under gas lubrication, and provide references for the textured design of piston rings in Stirling engines. A numerical simulation approach considering the deformation of the rings and the compressibility of the working medium was adopted to compare the effects of surface textures under both gas and liquid lubrication conditions. By varying parameters such as dimple diameter, area ratio and depth-to-diameter ratio, the load-carrying capacity map was drawn for dimple textures under both gas and liquid lubrication conditions, using the depth-to-diameter ratio and area ratio as coordinates, the influence mechanisms of dimple textures on gas and liquid lubrication were discussed, and the optimal parameters for each lubrication condition have been identified. The results showed there were significant differences between gas and liquid lubrication conditions. The load-carrying capacity in liquid lubrication mainly relied on the suppression of pressure drop through cavitation effects, while in gas lubrication, it primarily arises from the pressure difference between high-pressure and low-pressure regions. The load-carrying capacity maps indicated that the optimal depth-to-diameter ratio under liquid lubrication was larger, with values between 0.01 and 0.02, while for gas lubrication, it was smaller, around 0.005 to 0.010. The compressibility of gas allowed a larger high-pressure zone to be sustained, enabling significant load-carrying capacity even from a small area ratio 10% to a large area ratio 50%. Additionally the load-carrying capacity could be further enhanced by using an interlaced texture arrangement or increasing the spacing between textures, these two methods could provide a larger sustained range for high-pressure areas. In contrast, liquids were incompressible, high-pressure zone could not be sustained, thus liquid lubrication does not supported these methods and required a larger area ratio, with an optimal value around 40%.