Bending machine for bending a workpiece, said machine being of the type comprising a frame and a bending head, - the workpiece to be bent moving in a controlled manner at least axially relative to the frame, - said bending head moving transversely to the advance axis of the workpiece to be bent and supporting at least one bending roller (410,420) provided with a bending jaw, the roller ( 410, 420) defining a bending axis not parallel to the advance axis of the workpiece to be bent, - a bending arm being associated with said roller (410, 420) and rotating in a controlled manner about the bending axis, - at least one clamping member or clamping jaw, hereinafter called "mors", supported by the bending arm and arranged opposite the bending jaw with which it is to cooperate for the purpose of driving the portion of workpiece to be bent in a clamped manner between said mors (511, 512) and said jaw, said mors (511, 512) being movable in a controlled manner on the arm in order to clamp or unclamp said portion of the workpiece to be bent, - a ruler holder module, referred to as a ruler holder, sliding parallel to the advance axis of the workpiece to be bent and supporting at least two rulers (601, 602), arranged back-to-back, the workpiece to be bent being in contact with one ruler during the bending thereof, the ruler holder being driven and guided in translation on the bending head transversely to the advance axis of the workpiece to be bent, CHARACTERIZED BY THE FACT THAT said mors is supported by a mors holder accommodating at least two mors (511, 512) arranged back-to-back, the mors holder being fastened in a dismountable way to a shelf guided and driven in translation on the bending arm, the ruler holder is provided with punctual fastening means for punctually fastening the mors holder to accommodate the mors holder separated from the shelf and to move it on either side of the bending axis in its starting position transversely to the advance axis of the workpiece to be bent, independently of the bending arm so that the mors holder can be fastened again to the shelf once the bending arm is rotated 180 degrees. - the workpiece to be bent moving in a controlled manner at least axially relative to the frame, - said bending head moving transversely to the advance axis of the workpiece to be bent and supporting at least one bending roller (410,420) provided with a bending jaw, the roller ( 410, 420) defining a bending axis not parallel to the advance axis of the workpiece to be bent, - a bending arm being associated with said roller (410, 420) and rotating in a controlled manner about the bending axis, - at least one clamping member or clamping jaw, hereinafter called "mors", supported by the bending arm and arranged opposite the bending jaw with which it is to cooperate for the purpose of driving the portion of workpiece to be bent in a clamped manner between said mors (511, 512) and said jaw, said mors (511, 512) being movable in a controlled manner on the arm in order to clamp or unclamp said portion of the workpiece to be bent, - a ruler holder module, referred to as a ruler holder, sliding parallel to the advance axis of the workpiece to be bent and supporting at least two rulers (601, 602), arranged back-to-back, the workpiece to be bent being in contact with one ruler during the bending thereof, the ruler holder being driven and guided in translation on the bending head transversely to the advance axis of the workpiece to be bent, said mors is supported by a mors holder accommodating at least two mors (511, 512) arranged back-to-back, the mors holder being fastened in a dismountable way to a shelf guided and driven in translation on the bending arm, the ruler holder is provided with punctual fastening means for punctually fastening the mors holder to accommodate the mors holder separated from the shelf and to move it on either side of the bending axis in its starting position transversely to the advance axis of the workpiece to be bent, independently of the bending arm so that the mors holder can be fastened again to the shelf once the bending arm is rotated 180 degrees.