- Device for sheathing a shell on a so-called sheathing face of a hollow structure, the sheathing device comprising: a former having an outer face configured to conform all or part of the shape of the face of the hollow structure opposite the sheathing face and an inner face, the surface of the former being configured to allow air flow between the outer and inner faces thereof; a first suction mechanism for drawing air from the inner face of the former; and a frame at least partially surrounding the former and configured to hold a resilient membrane on the outer face of the former so as, in use, to sandwich the hollow structure and the shell between the outer face of the former and the resilient membrane and to fix the position thereof, characterized in that the sheathing device further comprises: a casing carrying a fluid-tight bladder arranged opposite the former, a fluid-tight system for injecting pressurized and thermoregulated fluid between the casing and the bladder, wherein the casing is movable between a position spaced from the former allowing the hollow structure, the shell and the resilient membrane to be installed on the former, and a working position in which the bladder, under the effect of the pressurized fluid, conforms to the shape of the outer face of the former and the structure in its various geometric details and applies pressure to the surface of the resilient membrane to press the shell against the sheathing face of the hollow structure and fix the position thereof. a former having an outer face configured to conform all or part of the shape of the face of the hollow structure opposite the sheathing face and an inner face, the surface of the former being configured to allow air flow between the outer and inner faces thereof; a first suction mechanism for drawing air from the inner face of the former; and a frame at least partially surrounding the former and configured to hold a resilient membrane on the outer face of the former so as, in use, to sandwich the hollow structure and the shell between the outer face of the former and the resilient membrane and to fix the position thereof, characterized in that the sheathing device further comprises: a casing carrying a fluid-tight bladder arranged opposite the former, a fluid-tight system for injecting pressurized and thermoregulated fluid between the casing and the bladder, wherein the casing is movable between a position spaced from the former allowing the hollow structure, the shell and the resilient membrane to be installed on the former, and a working position in which the bladder, under the effect of the pressurized fluid, conforms to the shape of the outer face of the former and the structure in its various geometric details and applies pressure to the surface of the resilient membrane to press the shell against the sheathing face of the hollow structure and fix the position thereof. a casing carrying a fluid-tight bladder arranged opposite the former, a fluid-tight system for injecting pressurized and thermoregulated fluid between the casing and the bladder, wherein the casing is movable between a position spaced from the former allowing the hollow structure, the shell and the resilient membrane to be installed on the former, and a working position in which the bladder, under the effect of the pressurized fluid, conforms to the shape of the outer face of the former and the structure in its various geometric details and applies pressure to the surface of the resilient membrane to press the shell against the sheathing face of the hollow structure and fix the position thereof.