A radial piston machine has a cylindrical housing which encloses a rotary shaft formed with an eccentric. A plurality of stationary piston rods is connected to the inner wall of the housing and radially directed toward the shaft. The free ends of piston rods are provided with ball-and-socket joints permitting universal rotary movement of the pistons. Each piston slidably engages the inner wall of an assigned cylinder which at its bottom wall slidably engages the eccentric. In a modification, the spherical surface of the stationary ball joint directly engages the inner wall of the cylinder.