A chuck assembly for use in a machine tool for holding a tool element comprises a chuck body 1 having a sleeve 4 integrally formed therewith, which sleeve has a support bore 5 defined therein for the receipt and support of the tool element and also has its outer peripheral surface 4a tapered in a direction away from the chuck body, a fastening screw 6 having its inner peripheral surface tapered in complemental relation to the outer peripheral surface of the sleeve and helically rotatably mounted on the sleeve through a plurality of roll bearings 8, and a reinforcing nut 20 threadingly mounted on the fastening screw. After the screw 6 has been turned helically in the nut 20 to tighten the chuck, the nut is then turned on the screw to clamp against the body 1. The sleeve socket 5 may take different forms (Figs. 2a-e). <IMAGE>
