An apparatus for producing wrapped bales comprises a wrapping device for circulating a web dispensing device in a first plane of rotation around a bale during a first wrapping stage. The surface of the web of wrapping material is kept substantially normal to the first plane of rotation. During a second wrapping stage, the bale may further be rotated by a rotating device in a second plane of rotation substantially normal to the first plane of rotation. Between the first and the second stages, the surface of the wrapping material web may be turned about 90° such that the surface of the web is always substantially normal to the planes of rotation in both stages. The first wrapping stage includes using a tunnel device, which makes it possible to produce both unbound wrapped bales and bound wrapped bales.