The invention concerns a protective sheath reclosable by overlapping comprising an outer longitudinal edge (10a) adapted to overlap an inner longitudinal edge (10b) of the sheath (10) in an overlap portion (13). Adhesive means (11) are fixed on an inner surface of the outer longitudinal edge (10a), the adhesive means (11) extending over a portion of the inner surface of the sheath (10) adapted to extend beyond the overlap portion (13). Said reclosable protective sheath is useful in particular for protecting at least an elongated object (15).