Abstract: A radial piston machine, such as a pump or a motor, has a housing in which a cylinder body is rotatable. The cylinder body has radial cylinder bores which accommodate reciprocable pistons. A shaft mounts the cylinder body for rotation and is formed with two axially spaced circumferential grooves between which it is also formed with a high-pressure control opening and with a diametrically opposite low-pressure control opening; these openings communicate intermittently with the inner ends of the cylinder bores. Sealing lands are formed on the shaft intermediate the grooves and the openings, and supporting lands are formed axially outwardly of the grooves.