A tyre for a vehicle wheel includes a carcass structure, belt structure, tread band, and at least one pair of sidewalls. The carcass structure includes at least one first carcass ply and at least two annular reinforcing structures. The at least one first carcass ply includes elongated sections circumferentially distributed around the tyre's geometric rotation axis. Each elongated section extends in a U-shaped configuration around a cross-section outline of the carcass structure to define two side portions and one crown portion. Each elongated section substantially lies in a plane parallelly offset relative to a meridian plane of the carcass structure. The crown portion of each elongated section is oriented, relative to a radial reference plane passing through a transition region between the crown portion and at least one corresponding side portion, at an angle having a different value from an inclination of the at least one corresponding side portion.