The invention relates to a device, called a fastening device (1), for fastening at least one object (2, 2') and a rigid rear shelf (3) of a motor vehicle (30), said fastening device (1) comprising: a link (4, 24) made of at least one elastic material, two hooks, a first hook (5, 5', 5'') attached to one of the two longitudinal ends of the elastic link (4) and a second hook (6, 6', 6'') attached to the other of the two longitudinal ends of the elastic link (4), each hook (5, 5', 5'', 6, 6', 6'') being shaped to cooperate with a through opening (7) formed in the rigid rear shelf (3) such that, each hook (5, 5', 5'', 6, 6', 6'') being engaged in a through opening (7) of the rigid rear shelf (3), the elastic link (4) is in a state of at least partial extension extends into contact with one of the two main faces (8,9) of the rigid rear tablet (3) in the absence of any object (2,2') interposed between the elastic link (4) and the rigid rear plate (3). Figure for the abbreviation: Fig. 5,