The invention concerns a double-sheath rigid pipe for transporting hydrocarbons consisting of two respectively inner (2) and outer (3) coaxial tubes separated by an annular gap (5), said pipe being adapted to be wound and comprising a device limiting the propagation of a deformation occurring on the outer tube, wherein a radial stop device (10) linked to the inner tube (2) but not linked to the outer tube (3) allows a localized collapse of value G of the outer tube, G being selected to stop the propagation of a deformation of the outer tube (3).