The hoop winding method allows to manufacture a reinforced tube by carrying out the following operations: depositing a reinforcing layer 2 around metal tube 1, then imposing a tensile force at the metal tube ends so as to plastically deform the metal tube by applying a pressure P2 in enclosure Z2, the force being determined to introduce a compressive stress in the metal tube after release of the force, and imposing a pressure P1 in enclosure Z1 in order to apply a pressure onto the inner wall of the metal tube so as to plastically deform the metal tube, the pressure being determined to introduce a compressive stress in the metal tube after release of the pressure. The fact that the two enclosures Z1 and Z2 are distinct and independent allows pressures P1 and P2 to be applied independently of one another. Thus, the method allows independent radial and axial prestresses to be applied so as to optimize the strength of the hoop-wound tube.