The carcass structure of a tire comprises one or more carcass plies each formed of strip lengths comprising longitudinal thread elements incorporated in a layer of elastomer material. The strip elements have respective crown portions disposed circumferentially in mutual side-by-side relationship, and side portions extending radially at the tire sidewalls. The side portions of each carcass ply are each at least partly covered with at least one of the side portions belonging to an adjacent deposition length. Associated with the carcass plies are annular structures comprising a pair of inextensible inserts in the form of an annulus which are anchored to the first and second carcass plies respectively and axially separated by an elastomeric filling body. A belt structure, a tread band, and sidewalls are combined with the carcass structure to define the tire.