The invention relates to a device for wrapping bodies, in particular harvested material bales (1) of hay, straw or wilted green crop, at least one wrapping material web being drawn off from a wrapping material supply (8) during the wrapping process and a means being provided which signals a tear in the wrapping material web or that the wrapping material supply (8) has been used up. In order to improve the device and to develop a simple and in particular cheaper solution, it is proposed according to the invention that at least one optical sensor (14, 15), ultrasonic sensor or sensor for electromagnetic waves/fields of different frequency ranges be associated with the wrapping material web portion (18) between wrapping material supply (8) and the body (1) and disposed stationarily.