Abrasive belt orbital grinding machine for round or elliptical tubes, with variable speed ideal for grinding, satin finishing and cleaning of parts with diameters from 10 to 150 mm both straight and folded. The processing takes place on the external surface, the piece does not rotate but is translated along the machine’s working axis, ensuring uniformity of results and minimum operator fatigue. The two abrasive belts contained inside the head on an orbital wheel have a tension and centering system. Prepared for the application of a feeder kit for the automatic advancement of the piece, with the possibility of returning the piece to the starting point and thus obtaining double processing. Prepared for the connection of a suction system that picks up the dust directly from the processing point.