The folding device has a locally fixed funnel roller (3) and a movable folding funnel (4). A flap (18) bridging the gap between the funnel roller and the upper edge (17) of the folding funnel is connected for swivel movement to the folding funnel. The web bearing face (19) of the flap touches on the funnel roller and the convex curved support face (20) mounted on the upper edge of the folding funnel is mounted on the flap to restrict the flap relative to the folding funnel. The convex curve support face is preferably ventilated.