Protective sheath for optical or electrical conductors hardened with respect to X-rays.It comprises a flexible sheath formed from a resin matrix containing in regularly dispersed powder form at least one metal and/or at least one inorganic compound of a metal, said metal having a high atomic number of at least 47, a covering placed between the optical fibre and the X-ray protection sheath and optionally a mechanical protection sheath made from plastic directly covering the optical fibre.