A tire for vehicle wheels includes a carcass, a tread strip, and a belt structure. The carcass has a central crown portion and two axially opposite sidewalls terminating in a pair of beads. Each bead includes at least one circumferentially unextendable annular reinforcing core having a series of spirals of metal wire radially superimposed and axially arranged alongside each other. The carcass has a reinforcing structure including at least one ply of rubberized fabric reinforced with metal cords lying in radial planes containing an axis of rotation of the tire. The reinforcing structure includes ends secured to the annular reinforcing cores and a neutral profile, lying in a radial cross-sectional plane, axially extending from bead to bead. The neutral profile intersects a cross section of a zone enclosing the annular reinforcing cores and has a continuous curvature devoid of inflection points along an extension between the beads.