Apparatus for fabricating a strip-like reinforcement structure for a tire, which includes a laying head for laying the strip. The laying head includes a guidance passage for the strip formed by slots, rolling-down rollers intended to cooperate with a form, a cutter for cutting the strip into separate arches, and a turning-over mechanism for turning over the strip about its own longitudinal axis for causing an opposite face of the strip to face the form. The turning-over mechanism includes a frame mounted on two bearings in a cradle of the laying head. The frame can turn through at least 180.degree. with respect to the cradle for inverting the strip.