The invention relates to a bending device for forming corrugations in a metal sheet including: a lower frame; an upper frame able to move vertically between a rest position and a bending position; at least two dies, carried by the lower frame; one being fixed with respect to the lower frame and the other mounted with the ability to slide; at least two punches carried by the upper frame; one being fixed and the other being mounted with the ability to slide on the upper frame; the bending device being designed so that, in operation, as the upper frame moves towards its bending position, the metal sheet transmits a pulling force to the sliding punch and to the sliding die which force moves them from a spaced-apart position toward a close-together position.