A ring for swaging constituted by a rolled-up length of metal strip whose two ends are bonded together without give rise to significant increased thickness in the bonding zone. The ends of the strip are disposed substantially in contact with each other via their terminal edges, and the thickness of each of said ends is close to half the thickness of the strip. The inside faces of the ends are offset outwardly relative to the inside surface of the ring so as to constitute a housing for a plate whose thickness is close to half the thickness of the strip. A set of complementary studs and holes is provided on the ends of the strip and on the plate, said studs being engaged in the holes and their free ends being riveted to the element opposite from the element carrying them.