The device comprises a pair of motorised slides (24) able to move back and forth along a bladeholder in the press. Each slide (24) comprises its own reference block (30) for engaging with the metal sheet that is to be bent. Each reference block (30) moves back and forth in its respective slide (24) towards and away from the bend line. Each slide (24) incorporates a movable toothed bar (46) and gearing (50) to convert the movements of the toothed bar (46) relative to the slide (24) into corresponding movements of the block (30) towards and away from the bend line. Each slide (24) incorporates selectively controllable means (60) for locking and releasing the toothed bar (46) relative to this slide. The device also comprises retaining means carried by the bladeholder for immobilizing the toothed bar in a predetermined position relative to the bladeholder. The arrangement is such that there is a biunivocal correspondence between, on the one hand, the positions of the slide (24) along its guide means when the toothed bar is immobilized in the above-mentioned predetermined position and, on the other hand, the position of the reference block (30) relative to the bend line.