Abstract: In a method for producing an inking roller in the form of a screen roller for an offset inking mechanism or similar ink applicator, during a scraping process a doctor blade slides over the surface of webs which define a screen system. A metal and/or hard ceramic layer, is applied to the roller cylinder, and a laser beam is used to burn a pattern into the abrasion-resistant, hydrophilic surface of the metal and/or ceramic layer. Hydrophobic lining material at least partly covers the walls of the depressions. A plurality of cells for receiving ink or the like are formed in the lining material of the fillable depressions and the arrangement and structure of the cells are independent of the arrangement and structure of the depressions.