A carcass structure for a two-wheeled vehicle tire includes at least one carcass ply and a pair of annular reinforcing structures. The at least one carcass ply includes a first series and at least one second series of strip sections circumferentially distributed in a mutually-alternated sequence around a geometric rotation axis of the tire. Each strip section includes longitudinal and parallel thread elements at least partly coated with at least one layer of elastomer material and extends in a substantially U-shaped configuration to define two side portions and a crown portion. The annular reinforcing structures are applied against end flaps of the first series of strip sections and are overlapped by end flaps of the at least one second series of strip sections. Each of the annular reinforcing structures includes an annular anchoring insert, including one or more elongated elements extending in radially-concentric coils, and at least one filling body.