A self-supporting tyre (1) has reinforcing structures at the beads (4) defining rest surfaces (4a) for a corresponding rim (1a) which have a profile converging towards the tyre rotation axis away from the equatorial plane (X-X) of the tyre itself. The carcass plies (3a, 3b) are each made by sequential deposition of strip-like sections circumferentially distributed on a toroidal support (11). Elastic-support inserts (16, 21) are interposed between the side portions (13a, 14a) of axially internal sections (13), axial intermediate sections (15). In this manner around at least one of said support inserts opening degree of which can be modulated depending on requirements, by modifying the land/empty space ratio determined by the distance existing between the side portions (13a, 14a, 15a) of the strip-like sections (13, 14, 15) covering each of the axially opposite sides of the support insert itself.