Abstract: The present invention relates to a method of thermally and mechanically protecting cables and bundles of cables by use of a sheath braided directly around the element to be protected using a braiding yarn constituted by a plurality of elementary strands formed by interlacing synthetic fibers obtained after cracking and spinning an aramid fiber and a carbonizable oxidized organic fiber. The carbonizable oxidized organic fiber constitutes the major portion of the synthetic fibers making up the elementary strand for the braiding yarn. The invention also provides a thermal and mechanical protective sheath for cables and bundles of cables obtained by the method. In order to improve certain mechanical or thermal characteristics of the sheath, it may be associated with a material made of a fiber additional to said two synthetic fibers, in order to form the elementary strand, or indeed the sheath braided in this way may itself be covered in additional braiding based on aramid fibers.