In a method and an arrangement for shimming a cylindrical magnet system, that has a cylindrical magnet having a bore therein with an axis extending therethrough, and a gradient coil assembly located within the bore, shimming is accomplished by stacking a number of planar pieces of shim material in each of said tubes, with each of the tubes having an axis parallel to the axis of the cylindrical magnet, and with the planar pieces of shim material and stacked in the tubes in respective planes that are perpendicular to the axis fo the cylindrical magnet.