In a tire for vehicles, the formation of each bead reinforcing structure envisages that, after laying of a first series of elongated sections defining axially inner terminal zones of a carcass ply, an annular anchoring insert consisting of a wire wound in axially adjacent turns is formed on an end portion directed axially towards the outside of the respective zone. A stiffening element tapering radially away from the axis of the tire is then formed on each inner terminal zone. A second series of elongated sections is then laid, completing the manufacture of the carcass ply with the formation of axially outer terminal zones which are superimposed on the stiffening elements. An additional annular insert is formed on an end portion of each outer terminal zone arranged radially superimposed on the anchoring insert. The tire according to the invention may be associated with a symmetrical rim which has two lateral portions designed to form the bead seats for engagement with the corresponding tire beads, which are defined by frustoconical surfaces converging towards the axis of rotation of the rim, away from the equatorial plane thereof.