Method for manufacturing a tyre, comprising: - a step of assembling a green form of the tyre during which an assembly is wound, around an assembly support that substantially exhibits symmetry of revolution about an axis of revolution (YY'), in the circumferential direction (XX') of the assembly support, the assembly comprising: o a first structure of first filamentary elements (64, 66), o a second structure of second filamentary elements (68, 70), the second structure of second filamentary elements (68, 70) being arranged radially on the inside of the first structure of first filamentary elements (64, 66), o a bearing structure comprising textile bearing filamentary elements connecting the first structure of first filamentary elements (64, 66) and the second structure of second filamentary elements (68, 70) to each other, each textile bearing filamentary element comprising at least one textile bearing filamentary portion extending between the first structure of first filamentary elements (64, 66) and the second structure of second filamentary elements (68, 70), - a step of moulding the assembled green form of the tyre during which the first structure of first filamentary elements (64, 66) is moved radially away from the second structure of second filamentary elements (68, 70), and - a step of heating the moulded green form of the tyre so as to at least partially crosslink the moulded green form of the tyre, which method is characterized in that, during the step of heating the moulded green form of the tyre, the tension in each textile bearing filamentary portion is zero. - a step of assembling a green form of the tyre during which an assembly is wound, around an assembly support that substantially exhibits symmetry of revolution about an axis of revolution (YY'), in the circumferential direction (XX') of the assembly support, the assembly comprising: o a first structure of first filamentary elements (64, 66), o a second structure of second filamentary elements (68, 70), the second structure of second filamentary elements (68, 70) being arranged radially on the inside of the first structure of first filamentary elements (64, 66), o a bearing structure comprising textile bearing filamentary elements connecting the first structure of first filamentary elements (64, 66) and the second structure of second filamentary elements (68, 70) to each other, each textile bearing filamentary element comprising at least one textile bearing filamentary portion extending between the first structure of first filamentary elements (64, 66) and the second structure of second filamentary elements (68, 70), o a first structure of first filamentary elements (64, 66), o a second structure of second filamentary elements (68, 70), the second structure of second filamentary elements (68, 70) being arranged radially on the inside of the first structure of first filamentary elements (64, 66), o a bearing structure comprising textile bearing filamentary elements connecting the first structure of first filamentary elements (64, 66) and the second structure of second filamentary elements (68, 70) to each other, each textile bearing filamentary element comprising at least one textile bearing filamentary portion extending between the first structure of first filamentary elements (64, 66) and the second structure of second filamentary elements (68, 70), - a step of moulding the assembled green form of the tyre during which the first structure of first filamentary elements (64, 66) is moved radially away from the second structure of second filamentary elements (68, 70), and - a step of heating the moulded green form of the tyre so as to at least partially crosslink the moulded green form of the tyre,