To form a sleeve with excellent forming accuracy and wear resistance at a low cost for an auto tensioner wherein a hydraulic fluid chamber in a cylinder is divided into a pressure chamber and a reserver chamber by inserting a piston into the sleeve in the cylinder.

A rod of free-cutting steel is cut and honing processed to scrape out the sleeve. The formed article is nitro-carburized to form a hard layer on a surface of the sleeve. The processing stress of the free-cutting steel is small, thereby deformation is not caused in the sleeve even by nitro-carburizing after processing and the sleeve is formed in the high accuracy. Further, the enhanced wear resistance is achieved by providing the hard layer on the surface.