Assembly for fastening an exhaust system suspension element to a support of the underbody of a motor vehicle

The device has a mounting stud support (1) and an exhaust pipe stud (3), each with an elastically deformable zone. A mounting bolt (5) fixes the support and the stud by tightening along a tightening direction (D). The support and stud have partial complementary profile in the respective elastic zones. The profiles are pressfitted to cooperate along the direction, and elastically deformed during the tightening of the bolt.