A first carcass ply (3a) is manufactured by laying down onto a toroidal support (11), a first and a second series of strip-like sections (13, 14) cut to size from a continuous strip-like element (2a) and each comprising longitudinal thread-like elements (17) incorporated into a layer of elastomer material (20). Sections (13) of the first series are sequentially laid down at a given circumferential distance from each other, to form side portions (13a, 14a) to the end flaps of which first primary portions (4a) of respective reinforcing structures (4) at the beads are applied. Sections of the second series (14) are each interposed between two sections of the first series (13), with the respective end flaps (14a) overlapping the primary portions (4a) of the annular structures (4). A second ply (3b) is manufactured in the same manner as the first ply, with a third and a fourth series of strip-like sections (15, 16) disposed in a crossed orientation relative to those of the first carcass ply and overlapping second primary portions of the annular reinforcing structures (4) on opposite sides. Additional portions (24) of the annular structures are applied to the end flaps (20a) of sections (14) belonging to the second series.