Method and apparatus for building a cord or wire wound carcass for a closed torus tire. An endless flattened inflatable tube providing a liner for the carcass and coaxially spaced bead rings are placed on a support comprising a cylindrical array of rolls. The bead rings are spaced axially to control the length of each turn of cord or wire wound in the flattened oval path around them. A single wire or cord is wound in a flat oval orbit about the liner and bead rings by orbiting a spool along a track having two straight parallel portions, one inside, the other outside the bead rings and liner. The parallel track portions are connected at their ends by semi-circular track portions. No rigid core is required. After winding the cord or wire about the liner and bead rings, the liner is inflated and the bead rings are shifted axially toward each other to the axial spacing appropriate for the inflated tire in use.