The invention relates to a method for ink supply to ink trays in printing presses, whereby the printing press has for ink supply an ink tray, which is adjoined with an in ball cooperating with ink dosing elements. Task of the invention is to provide a method and an apparatus for zonal ink dosage according to the ink requirements and an extensive residue-free emptied ink tray at job end or job change. The task is solved according the invention by stopping the ink supply before the end of the printing job. This moment is determined so, that a minimum amount of ink sufficient for the to be processed product volume remains in the ink tray at the pre-determined job end and the ink is shifted from ink zones or ink zone groups with lesser ink consumption to ink zones or ink zone groups with momentarily higher ink consumption for processing of the remaining printing job.