The subject of the invention is the device for pulling out a single tyre from a tyre bundle the device has (having) a frame (1) which has slide guides on which a moveable clamp of the stretcher (3) moves, and between which there is a horizontally attached fixed clamp of the stretcher (2) and a vertically attached prop (4), which has an arm (5) on its end powered by a driving element and having a catching or hooking element at the end(8). The second subject of the invention is the method of unpacking tyres