A screw-shaped anchoring element for permanent anchorage of hearing aid devices or ear and eye prostheses in the skull bone. A main body including external threads has a length less than 5 mm and is operative to be inserted into a hole in a skull bone. A flange is operative to provide a stop for the anchoring element when the anchoring element is screwed down into the comparatively thin skull bone. The flange has a substantially planar bottom surface for resting against the skull bone when the anchoring element has reached a final screwed-down position. A tool engaging socket is arranged at one end of the anchoring element. An inner bore extends at least partially through the main body at the first end of the anchoring element and is operative to connect one of a hearing aid device, an eye prosthesis or an ear prosthesis to the anchoring element. A self-tapping second end of the anchoring element includes at least one cavity and a cutting edge. The at least one cavity has a total volume corresponding to at least half a volume of bone tissue material that could be cut off by the cutting edge when the anchoring element is screwed down into a hole in the skull bone with a diameter corresponding to an inner diameter of the screw thread.