A tyre for a vehicle wheel includes a carcass structure, a belt structure, a tread band, and sidewalls laterally applied to opposite sides of the carcass structure. The carcass structure includes at least one carcass ply with a first and second series of strip segments and a pair of annular reinforcing structures. In one embodiment, each of the pair of annular reinforcing structures includes a first annular insert having opposed axial surfaces and being positioned between respective lateral portions of the first series of strip segments and respective diverging lateral portions of the second series of strip segments. In this embodiment, no filling body is positioned between the respective lateral portions of the first series of strip segments and the respective diverging lateral portions of the second series of strip segments. In an alternative embodiment, each of the pair of annular reinforcing structures includes a first annular insert and a filling body, the first annular insert and the filling body each having opposed axial surfaces and being positioned between the respective lateral portions of the first series of strip segments and the respective diverging lateral portions of the second series of strip segments.