The invention relates to a method for the computer-assisted manufacturing of a tooth replacement part or a dental auxiliary element from a blank, which can be rotated about an axis of rotation (10), by means of a machine tool, wherein a blank data set (8) comprising the axis of rotation (10) and a model data set (1) of the tooth replacement part or dental auxiliary element are stored and the model data set (1) has a first region (4) having a first insertion axis (5) and a second region (6) having a second insertion axis (7) askew to the first insertion axis (5), wherein in a first positioning step (S1) the model data set (1) is arranged in the blank data set (8) in such a way that the first insertion axis (5) of the model data set (1) is oriented perpendicular to the axis of rotation (10) of the blank data set (8) and in a second positioning step (S2) the second insertion axis (7) of the model data set (1) is oriented perpendicular to the axis of rotation (10) of the blank data set (8) by rotating the model data set (1) about the first insertion axis (5).
