The present invention relates to a wrapping device (1) configured to wrap a bale (12) with a wrapping material (2), wherein the device (1) comprises a wrapping unit (3) which is rotatable clockwise and counterclockwise and which is configured to wrap part of the bale by rotating the wrapping unit (3) counterclockwise around the bale and to wrap another part of the bale by rotating the wrapping unit (3) clockwise around the bale. By means of such a device, it is possible to wrap a bale without using a welding device. By means of such a device, it is also possible to use not readily weldable wrapping material (such as e.g. tape fabric made from PP or PE).
