This abutment device for the precision positioning of sheet-plates in a machine tool such as a shear or a bending-press comprises a pair of abutment arms movable depthwise for determining the sheet-plate position; these arms being each carried by a separate carriage adapted to be moved independently on a common transverse guide rail comprising two series of driving means for moving said carriage along said rail and the corresponding abutment arms depthwise, each carriage comprising two series of braking means for holding the carriage against movement on said rail and the relevant abutment arm on said carriage.