A tire for a vehicle wheel is provided which comprises a carcass structure, and a belt structure applied to the carcass structure at a circumferentially-outer position of the carcass structure. A tread band is also provided which is circumferentially superposed on the belt structure, and sidewalls are laterally applied to opposite sides of the carcass structure. The carcass structure comprises at least one carcass ply, and a pair of annular reinforcing structures, wherein the at least one carcass ply comprises a first series and a second series of strip segments consecutively arranged along a circumferential development of the carcass structure, and each strip segment extends according to a substantially U-shaped conformation. In addition, each strip segment comprises at least two filiform elements, positioned longitudinally and parallel to each other, and at least partially coated by at least one layer of elastomer material. Also, each annular reinforcing structure is engaged in proximity to a respective inner circumferential edge of the at least one carcass ply. Each annular reinforcing structure comprises at least one primary portion, and at least one additional portion, wherein the at least one primary portion comprises an axially-inner side oriented toward terminal edges of the first series of strip segments, and the at least one primary portion comprises an axially-outer side oriented toward terminal edges of the second series of strip segments. Further, the at least one primary portion comprises a first circumferentially-inextensible annular insert, a filling body, and at least one second circumferentially-inextensible annular insert, wherein the first annular insert is substantially annulus-shaped, is positioned coaxially to the carcass structure, adjacent to the respective inner circumferential edge of the at least one carcass ply, and is formed by at least one elongated element extending in concentric turns. Moreover, the filling body is made of elastomeric material, and is joined to the first annular insert. The at least one second annular insert is substantially annulus-shaped, and is positioned coaxially to the carcass structure, axially side-by-side to the filling body and laterally opposite relative to the first annular insert, wherein the at least one second annular insert is formed by at least one elongated element extending in concentric turns, the at least one additional portion is positioned against the terminal edges of the second series of strip segments on a side opposite to the at least one primary portion, the at least one additional portion comprises at least one third circumferentially-inextensible annular insert, the at least one third annular insert is substantially annulus-shaped, the at least one third annular insert is positioned coaxially to the carcass structure, adjacent to the respective inner circumferential edge of the at least one carcass ply, and the at least one third annular insert is formed by at least one elongated element extending in concentric turns,