An edge-covering material and a process for preventing undesirable ridges from exposure of laser-processible, photopolymerizable printing plates premounted on sleeves or cylinders is disclosed. The edge-covering material containing at least one soluble, film-forming polymer, at least one UV absorber, and a solvent or a solvent mixture is applied on the edges of the photo-polymerizable printing plate before imagewise exposure of the photopolymerizable printing plate.