A wrapping over device for use with a rotatable solid body tire assembly drum. The wrapping over device includes an arcuate support having at least three conical finger elements mounted thereon. The finger elements are positioned progressively closer to an axial centerline of the tire assembly drum in a direction of rotation of the drum. A pressing roller is rotatably mounted on the support at a position between the conical fingers. A pivot drive pivotally mounts the support for rotation about an axis disposed at right angles to the assembly drum axial centerline. A parallel drive means mounts the pivot drive means for movement in a direction parallel to the tire assembly drum axial centerline.