Abstract: A machine for spirally wrapping a continuous element, such as a cord or tape, around an annular tire bead. The machine is provided with a mechanism for holding a tire bead and rotating it in a fixed plane and at a predetermined speed, while a device with the element rotates about the rotating bead to wrap a portion of the continuous element around the bead at a speed which is correlated to the rotational speed of the tire bead so that the finished tire bead has a predetermined spiral wrap which can be varied by changing the relative rotational speeds of the tire bead and element about the tire bead. The machine is supplied with a braking mechanism which is designed to cushion the stop of the bead wrapping mechanism, rather than bringing it to an abrupt halt, and to bring the bead wrapping mechanism always to a halt at a desired position for beginning the wrapping of another bead. A knife is furnished for cutting the continuous element after the bead wrapping operation is completed and the machine is stopped.