A high-speed drill or milling machine has a tool that is secured in a central aperture (5) by a chuck (2) with one or more interface grooves (6) open to the tip. A wedge (9b) engages axially with the groove (6) from the open tip. The sleeve (10) around the groove (6) is partly elastic and is deformed outwardly under pressure when the wedge (9b) is inserted in the groove (6).