A method of manufacturing a tire for a vehicle wheel includes making a carcass structure, applying a belt structure to the carcass structure, applying a tread band to the belt structure, and applying at least one pair of sidewalls to the carcass structure. Making the carcass structure includes applying at least one first part of the at least one carcass ply on a toroidal support, applying at least one circumferentially-inextensible annular anchoring insert, and applying at least one stiffening element. The at least one annular anchoring insert includes a cross-sectional profile of flattened conformation, extending away from an equatorial plane of the tire. The at least one stiffening element includes at least one main portion with a cross-sectional profile tapering away from a rotation axis of the tire. The at least one main portion is located substantially at an axially-inner position relative to the at least one annular anchoring insert.