Abstract: A method of clamping a rotationally symmetrical body (10) for the purpose of machining, in which method the body (10), with its first side (12), is pulled by means of a tensile force (F1), which acts in extension of the rotation axis (19, 19?) of the body (10) on the first side (12) of the body (10), against a supporting element (72) having a centering effect. A device for clamping a rotationally symmetrical body (10) for the purpose of machining, which device comprises a supporting element (72), against which the body (10) can be pulled, and a tie rod (64) which can act on and pull the body (10), to be clamped, axially and concentrically to the rotation axis (19, 19?) of the latter. The mounting of the tie rod (64) is designed in such a way that the tie rod (64) is axially guided with radial clearance (66) for the axial pulling movement. The tensile force (F1) of the tie rod (64) is preferably adjustable.