The present invention relates to a process for producing a surface structure, preferably on a cylinder, cylinder dressing, or roller of a printing machine, with a hard chromium coating which is galvanically produced and preferably ground to dimensional accuracy. The object of the invention is to develop a process which permits a surface structure to be produced on the hard chromium coating, which surface structure permits relatively high frictional forces between the contact points of the printing material and the coating of the cylinder of the printing machine. This is achieved in that the surface structure is produced in two process steps in sequence, a surface part structure being produced as a dot screen in an approximately even random distribution by means of a first material erosion process in a first process step, and the final surface structure being produced in a second process step by means of a second material erosion including the dot screen.