A bending device for forming a corrugation in a metal sheet intended for the construction of an airtight membrane of a fluid storage tank, the bending device comprising: - a lower frame; - a lower die having a first and a second die element (14, 15), each having a bearing surface for the metal sheet and a concave half-impression, the first and second die elements (14, 15) each being mounted so as to slide on the lower frame in a direction x, so as to be able to slide between a far position and a near position, the half-impressions of the first and second die elements (14, 15) together defining an impression corresponding to the shape of the corrugation being formed when the first and second die elements (14, 15) are in their near position, said first and second die elements (14, 15) being returned to their far position by a first return unit; - an upper punch, arranged above the lower die, comprising a lower end provided with a head having a shape complementary to that of the impression, said upper punch being able to move vertically with respect to the lower frame between a position of rest and a bending position in which the head of said upper punch is engaged inside the impression of the lower die so as to press on the metal sheet; and - a first and a second side clamp (17, 18), extending on either side of the upper punch, above the lower die, respectively facing the first and the second die elements (14, 15), said first and second side clamps (17, 18) being mounted able to slide in the direction x between a near position and a far position and being returned to their far position by a second return unit; the first and the second side clamps (17, 18) being able to move vertically with respect to the lower frame between a released position and a clamping position in which the first and the second side clamps (17, 18) are respectively brought near the bearing surface of the first die element and that of the second die element so as to clamp the metal sheet against the bearing surface of the first and the second die elements (14, 15) so that, during operation, when the metal sheet is clamped between the side clamps (17, 18) and the die elements (14, 15), the displacement of the upper punch from its position of rest toward its bending position causes a bending of the metal sheet, during which the metal sheet transmits a traction force in the direction x to the die elements (14, 15) and to the side clamps (17, 18) and thus displaces the die elements (14, 15) and the side clamps (17, 18) into their near position. - a lower frame; - a lower die having a first and a second die element (14, 15), each having a bearing surface for the metal sheet and a concave half-impression, the first and second die elements (14, 15) each being mounted so as to slide on the lower frame in a direction x, so as to be able to slide between a far position and a near position, the half-impressions of the first and second die elements (14, 15) together defining an impression corresponding to the shape of the corrugation being formed when the first and second die elements (14, 15) are in their near position, said first and second die elements (14, 15) being returned to their far position by a first return unit; - an upper punch, arranged above the lower die, comprising a lower end provided with a head having a shape complementary to that of the impression, said upper punch being able to move vertically with respect to the lower frame between a position of rest and a bending position in which the head of said upper punch is engaged inside the impression of the lower die so as to press on the metal sheet; and - a first and a second side clamp (17, 18), extending on either side of the upper punch, above the lower die, respectively facing the first and the second die elements (14, 15), said first and second side clamps (17, 18) being mounted able to slide in the direction x between a near position and a far position and being returned to their far position by a second return unit; the first and the second side clamps (17, 18) being able to move vertically with respect to the lower frame between a released position and a clamping position in which the first and the second side clamps (17, 18) are respectively brought near the bearing surface of the first die element and that of the second die element so as to clamp the metal sheet against the bearing surface of the first and the second die elements (14, 15) so that, during operation, when the metal sheet is clamped between the side clamps (17, 18) and the die elements (14, 15), the displacement of the upper punch from its position of rest toward its bending position causes a bending of the metal sheet, during which the metal sheet transmits a traction force in the direction x to the die elements (14, 15) and to the side clamps (17, 18) and thus displaces the die elements (14, 15) and the side clamps (17, 18) into their near position.