A laser cutting machine including an X1 axis provided with clamps which make it possible to firmly grip a material to be cut in sheets or on reels (the blank) enabling the material to be moved from left to right; a Y-axis: perpendicular to the X1 axis, enabling the movement of a laser cutting head; an X2 axis with at least one pair of clamping rollers enabling the material to be moved to the left or to the right; a straightening/de-cambering/levelling system placed beside this X2 axis comprising an optimised number of rollers; a unit incorporating the X2 axis and the straightening system which can be moved upwards or downwards, and a motorized discharge table enabling the cut elements (scrap and good pieces) to be discharged at a precise point, delimiting a picking zone.