A rotary cutting tool having a cutting element at one end and a cylindrical shank at the other end terminating in a T-shaped mounting tongue member, and a tool support for holding the tool in floating engagement the support having a cylindrical body with a transverse T-slot in its end for receiving said tongue member, the slot having sliding clearances with respect to the tongue member, and the holder having a sleeve which is spring urged to cover the T-slot to retain the tongue member in it, the inner diameter of the bore through the sleeve having a small clearance where it overlies the shank of the tool so that the latter can move transversely to align the tool in a hole when it is in use.