The invention relates to a tool for machining a work piece, comprising a holder (1) having a receiving opening (11) arranged on the front and a cutting head (5) having at least one cutting element (41) arranged at the end on the work piece side. The tool further comprises a shell (2) substantially made of hard metal, said shell being inserted with accurate fit into the receiving opening (11) of the holder (1) with a first end (22) on the holder side and being arranged in or on the second end (23) of the cutting head (5) on the cutting head side. The invention further relates to coupling means (6, 25) for coupling the holder, cutting head and shell.