a sleeve that is radially expandable under the action of an inflation fluid in order to be pressed hermetically against the wall of the pipe or the well, the sleeve being fastened to end members,

wherein said sleeve comprises:

firstly a pair of cylindrical membranes having walls that are flexible and elastic, the membranes being engaged coaxially one in the other and comprising an inner membrane for being subjected internally to the pressure of the inflation fluid and an outer membrane for being pressed against the wall of the pipe or the well in order to seal it off, and

secondly at least one very dense annular fiber structure formed of a multitude of fine and long fibers having high mechanical strength interconnecting said end members and wound helically about the inner membrane along an axis that coincides with the longitudinal axis of symmetry of the sleeve, and

wherein said fiber structure firstly presents a certain thickness and secondly is interposed between said membranes, and

wherein the winding angle of the fibers relative to the direction of said longitudinal axis of symmetry has a value that is considerably greater in the end portions of the sleeve than in the central portion thereof, the transition between the two portions taking place progressively over transition zones, with the angles taking on an intermediate value, the winding being such that the density of the fibers progressively diminishes from each end going towards the central portion, the angle of inclination of the fibers before expansion being calculated slice by slice in such a manner that in each of the annular slices of the fiber structure the shortening ratio after radial expansion of the sleeve is substantially constant over the entire thickness of said slice.