Abstract: The invention relates to such a method and apparatus, as well as to the resulting deformed object out of a relatively hard material such as e.g. a metal or plastic wire in which an undeformed section (2) is clamped near its ends (3, 4) and is subsequently upset in a controlled way by an axial pressure force (22) to a predefined shortened and thickened longitudinal section (5), with which simultaneously over substantially the entire contour sheath (19) of this section (2) a counterforce (29) is exerted so that, with the progressive deformation during upsetting, the total volume of the longitudinal section that is deforming, remains substantially constant. In this thickened section (5) a flattened zone (8) can subsequently be applied in order to realise a final shape (10) such as an opening (26). The invention concerns in particular also the use of a deformation line (40) for manufacturing a heddle for weaving looms.