A device made up of a textile tubular sheath, which can be implanted in the human body, suitable for containing a filling material and the ends of which are suitable for covering the ends of two portions of a single resected rib. The sheath contains a braid, in which the yarns allow relative movement in relation to one another in order locally to modify the diameter and the shape of the braid, such that the braid not only covers but also encloses the end of one portion of the rib. The sheath is secured to a tip which, allowing the injection of a biocompatible material for filling the sheath, the packing of the braid and the connection by adhesion of the sheath and the braid with the ends of the portions of the rib, is in turn sectional.