The invention relates to a holding or immobilising device shaped so as to surround a limb or a joint of a user, comprising an elastic bandage (1) having two bandage sections (10, 20) exhibiting different levels of stiffness, the elastic bandage comprising an inner face (15) which is in contact with an area covered by the bandage and an outer face (14) opposing the inner face, the inner face of the bandage adhering to the covered area, in the presence of an immobilising pressure exerted when the bandage is arranged tightly around a limb or a joint, such that the two bandage sections can maintain stretching resulting from different stretching forces, once said stretching forces have disappeared.
