A wrapping apparatus wraps an object (B) into wrapping material. The object (B) is carried on a wrapping table (49) while being wrapped. A wrapping part rotating motor (20, 51) rotates the wrapping table (40) carrying the object (B). A web (57) is pulled from a reservoir (58). When the rotation is stopped, a locking device (1, 3, 4) is transferred from a releasing mode into a locking mode and locks the wrapping table (49) selectively in a defined unloading rotational position or in a further rotational position.
