Assistance system for fitting a medical compression device onto a limb of a patient, the medical compression device having a fitting opening, with the assistance system comprising: - a support extending along a longitudinal axis, - two stretching members each comprising a connecting arm extending from the support along a first transversal direction, and a body extending from the connecting arm along a second transversal direction, with the body of each one of the stretching members comprising a base linked to the connecting arm and at least one retaining part (39a, 39b) separated from the base and whereon at least one portion of the medical compression device in the vicinity of the fitting opening is intended to be positioned, with the stretching members being mounted on the support facing one another and which can be displaced with respect to one another in translation along the longitudinal axis, the assistance system being characterised in that the retaining part (39a, 39b) and the base of at least one, first, of the stretching members extend respectively in transverse planes (Pt1, Pt2, Pt3) perpendicular to the longitudinal axis, with the transversal plane (Pt1, Pt2) containing the retaining part (39a, 39b) of the first stretching member being offset along the longitudinal axis towards the retaining part (39a, 39b) of the other, second, stretching member relative to the transversal plane containing the base of said first stretching member, the body of the first stretching member having a recess along the second transversal direction at least on the retaining part (39a, 39b), and in that the first stretching member comprises: - a shaped rod for forming the body and comprising the base of the body, - an external connecting element extending along the first transversal direction for forming a part of the connecting arm, the base of the body being linked to the external connecting element, and - an internal connecting element extending along the first transversal direction parallel to the external connecting element, the internal connecting element being separated from the external connecting element along the longitudinal axis in the direction of the second stretching member, the internal connecting element forming another part of the connecting arm to which the rod is linked opposite the base. - a support extending along a longitudinal axis, - two stretching members each comprising a connecting arm extending from the support along a first transversal direction, and a body extending from the connecting arm along a second transversal direction, with the body of each one of the stretching members comprising a base linked to the connecting arm and at least one retaining part (39a, 39b) separated from the base and whereon at least one portion of the medical compression device in the vicinity of the fitting opening is intended to be positioned, with the stretching members being mounted on the support facing one another and which can be displaced with respect to one another in translation along the longitudinal axis, - a shaped rod for forming the body and comprising the base of the body, - an external connecting element extending along the first transversal direction for forming a part of the connecting arm, the base of the body being linked to the external connecting element, and - an internal connecting element extending along the first transversal direction parallel to the external connecting element, the internal connecting element being separated from the external connecting element along the longitudinal axis in the direction of the second stretching member, the internal connecting element forming another part of the connecting arm to which the rod is linked opposite the base.