A sheet metal forming device intended to form a bend in a corrugation, the forming device comprising: a bottom frame having a planar mounting surface intended to receive a sheet metal plate having a corrugation that needs to be bent, the corrugation that needs to be bent projecting relative to a planar portion of the sheet metal plate, a projecting counter-form arranged on the mounting surface and intended to be accommodated in the corrugation that needs to be bent, the projecting counter-form having a stationary portion and a movable portion that is hinged, relative to the stationary portion, about an axis perpendicular to the mounting surface, a top frame arranged above the bottom frame, a press configured to lower the top frame towards the bottom frame, and a hollow upper die carried by the top frame between the top frame and the bottom frame, the hollow upper die being arranged above the movable portion of the projecting counter-form, the upper die comprising: an inner side half-die that has a planar bottom surface parallel to the mounting surface and an inner imprint side surface intended to delimit a sidewall of the corrugation situated on the inside of the bend, the inner imprint side surface having a longitudinal axis parallel to the planar mounting surface, and an outer side half-die that has a planar bottom surface parallel to the mounting surface and an outer imprint side surface intended to delimit a sidewall of the corrugation situated on the outside of the bend, the outer imprint side surface having a longitudinal axis parallel to the longitudinal axis of the inner imprint side surface, the hollow upper die being oriented or orientable relative to the bottom frame such that the longitudinal axes of the inner and outer imprint side surfaces form a bending angle with respect to the stationary portion of the projecting counter-form, the hollow upper die being coupled to the top frame in order to transmit the force of the press towards the bottom frame. a bottom frame having a planar mounting surface intended to receive a sheet metal plate having a corrugation that needs to be bent, the corrugation that needs to be bent projecting relative to a planar portion of the sheet metal plate, a projecting counter-form arranged on the mounting surface and intended to be accommodated in the corrugation that needs to be bent, the projecting counter-form having a stationary portion and a movable portion that is hinged, relative to the stationary portion, about an axis perpendicular to the mounting surface, a top frame arranged above the bottom frame, a press configured to lower the top frame towards the bottom frame, and a hollow upper die carried by the top frame between the top frame and the bottom frame, the hollow upper die being arranged above the movable portion of the projecting counter-form, the upper die comprising: an inner side half-die that has a planar bottom surface parallel to the mounting surface and an inner imprint side surface intended to delimit a sidewall of the corrugation situated on the inside of the bend, the inner imprint side surface having a longitudinal axis parallel to the planar mounting surface, and an outer side half-die that has a planar bottom surface parallel to the mounting surface and an outer imprint side surface intended to delimit a sidewall of the corrugation situated on the outside of the bend, the outer imprint side surface having a longitudinal axis parallel to the longitudinal axis of the inner imprint side surface, an inner side half-die that has a planar bottom surface parallel to the mounting surface and an inner imprint side surface intended to delimit a sidewall of the corrugation situated on the inside of the bend, the inner imprint side surface having a longitudinal axis parallel to the planar mounting surface, and an outer side half-die that has a planar bottom surface parallel to the mounting surface and an outer imprint side surface intended to delimit a sidewall of the corrugation situated on the outside of the bend, the outer imprint side surface having a longitudinal axis parallel to the longitudinal axis of the inner imprint side surface, the hollow upper die being oriented or orientable relative to the bottom frame such that the longitudinal axes of the inner and outer imprint side surfaces form a bending angle with respect to the stationary portion of the projecting counter-form, the hollow upper die being coupled to the top frame in order to transmit the force of the press towards the bottom frame.