A method and apparatus are described, which permit a simple, rapid manufacture of an end of an optical fiber bundle. According to the method a metallic sleeve is placed on an end section of the bundle, the end section with the sleeve on it is positioned in a shaping tool without pressing the sleeve and then pressure is exerted on the sleeve exclusively in a radial direction by press jaws of the shaping tool. In the optical fiber bundle made by the method the outer optical fibers (4') of the optical fiber bundle (1) are embedded at least partially in the sleeve material. The apparatus for making the end of the bundle (1) with the sleeve (10) has a shaping tool (20) including at least two radially movable press jaws (22a-22f) that substantially surround the sleeve (10).