The polisher shuttle serves to polish the inside walls of cylindrical tubes, in particular tubes for medical use. It comprises radial projections that are flexible along the axial direction, suitable for polishing the inside walls of tubes merely by relative movement between the shuttle and the tube, the shuttle passing inside the tube. In a longitudinal section, the sections of the projections form a series of separate undulations that are long and thin in the radial direction. The polishing method made possible by the shuttle is particularly simple, since a single pass of the shuttle can suffice for performing polishing; the method is thus fast and easy to automate, e.g. in a polisher device of the invention.