For the attachment of a tool provided with a cylindrical or frusto-conical shank to a rotating machine spindle at one end of the machine spindle a complementary reception opening for the shank is provided. The shank contains a coaxial bore and a plurality of slots distributed in the circumferential direction and extending through radially to the bore, which divide the shank within the reception opening into segments. In the region of the slots the shank widens out under the influence of centrifugal forces more than does the region of the spindle surrounding the shank. Thus the radial guidance of the tool is not lost even at very high rotation rates of 10,000 r.p.m. and above. A support shoulder on an annular collar of the tool prevents axial reshifting of the shank by reason of the axial stress of a clamping device and improves the rigidity of the tool-spindle connection. The bore extends through the annular collar. The external diameter of the annular collar is preferably made larger than according to standard. The end face of the spindle, intended to abut on the support shoulder, is radially inwardly provided with an annular recess and supports the tool on a maximum possible diameter. In addition a shape-engaging coupling can be provided between tool and spindle.