A low-section tire includes an air tube including an internal wall and two air tube sidewalls. The internal wall comprises a greater rigidity than the tube sidewalls so that, when a carcass and the tube are mounted on a rim, and during inflation, the tube sidewalls contact the carcass sidewalls no later than the internal wall contacts a crown portion of the carcass. A process for manufacturing the air tube includes moulding two tube sidewalls separated from each other, moulding a central core, arranging the tube sidewalls and central core in a single vulcanization mould, closing the vulcanization mould to form the tube, feeding pressurized fluid into at least two distinct circumferential portions of the tube, and vulcanizing the tube to join the central core and tube sidewalls. A mould for manufacturing the an air tube includes two axially-external cheeks, two axially-intermediate male dies, and two axially-inner spacers.