After ink remaining on an ink supply roller (R) for applying ink onto a plate cylinder is softened by a solvent, a washing cloth (4) is brought into pressure contact with the ink supply roller and is moved either intermittently or continuously so as to let the softened ink soak into and be held in an oil absorption layer of the washing cloth. After soaked with ink, the washing cloth is sent into a processing portion (8) and is cut by a cutter (3) or taken up in a predetermined length by a take-up roller and then discarded together with the roller. The washing cloth has at least the oil absorption layer and an oil impermeation layer, has high absorptivity of the softened ink and does not permit leak of the absorbed ink. Particularly in the washing cloth having an oil permeation layer which does not permit the back-flow, the absorbed ink is completely held in the absorption layer and this washing cloth is extremely easy to handle. Furthermore, in the washing cloth which contains an oil coagulant in the absorption layer, the absorbed ink is solidified or gelatinized by cooling after heating, and subsequent processing of the washing cloth becomes simple.