Apparatus for wrapping a piece to be wrapped with a wrapping material, which is arranged to run around a wrapping track forming a guide for the apparatus in such a way that the apparatus is arranged to travel along the wrapping track and which wrapping track is arranged to run through a centre hole of the piece to be wrapped, and which apparatus includes - an assembly, - a discharge arrangement at least partly fitted to the assembly for a wrapping-material source, which includes - a support-element arrangement for the wrapping-material source, from which the wrapping material is arranged to be discharged, - drive means including an operating device (13, 33) fitted to the assembly and arranged to act on the wrapping-material source, in order to maintain the tension in the wrapping material arranged to be discharged from it, - measuring means for detecting the tension of the wrapping material, from which a feedback is arranged to the drive means, - a guide arrangement through which the wrapping material is arranged to be led from the support-element arrangement to the piece to be wrapped, characterized in that - the guide arrangement includes only a single deflector roll in order to achieve only a single change of direction in the wrapping material between the piece to be wrapped and the support-element arrangement, - the tension of the wrapping material is arranged to be detected from the discharge arrangement - the feedback is internal in which the drive means include a control unit of the operating device (13, 33) arranged to act as the said measuring means, and in which the tension of the wrapping material is arranged to be detected from the actual value of the current of the operating device (13, 33). - an assembly, - a discharge arrangement at least partly fitted to the assembly for a wrapping-material source, which includes - a support-element arrangement for the wrapping-material source, from which the wrapping material is arranged to be discharged, - drive means including an operating device (13, 33) fitted to the assembly and arranged to act on the wrapping-material source, in order to maintain the tension in the wrapping material arranged to be discharged from it, - a support-element arrangement for the wrapping-material source, from which the wrapping material is arranged to be discharged, - drive means including an operating device (13, 33) fitted to the assembly and arranged to act on the wrapping-material source, in order to maintain the tension in the wrapping material arranged to be discharged from it, - measuring means for detecting the tension of the wrapping material, from which a feedback is arranged to the drive means, - a guide arrangement through which the wrapping material is arranged to be led from the support-element arrangement to the piece to be wrapped, - the guide arrangement includes only a single deflector roll in order to achieve only a single change of direction in the wrapping material between the piece to be wrapped and the support-element arrangement, - the tension of the wrapping material is arranged to be detected from the discharge arrangement - the feedback is internal in which the drive means include a control unit of the operating device (13, 33) arranged to act as the said measuring means, and in which the tension of the wrapping material is arranged to be detected from the actual value of the current of the operating device (13, 33).