A green tire has a symmetric profile in radial section having a radially outer tread band, two radially inner beads and two sidewalls each extended from one edge of the tread band to one of the beads. During a molding and vulcanization treatment of the green tire, a movement is imposed to the tread band with respect to the beads along a direction parallel to a rotation axis of the tire, to obtain a molded and vulcanized tire having an asymmetric profile in radial section. A mold for vulcanizing tires for vehicle wheels is also described, having a tread wall axially asymmetric with respect to a middle line plane of the mold.