A photosensitive recording material having a dimensionally stable substrate and a photosensitive layer which is applied thereon and containsA) an elastomeric block copolymer as a binder,B) a polymerizable compound andC) a compound capable of initiating the polymerization of the compound B under the action of actinic radiation,is described, the elastomeric block copolymer A being a block copolymer having blocks of polymerized1. styrene units,2. alkylene units and3. diene units.The material is suitable for the production of relief printing plates, especially flexographic printing plates, which are distinguished by higher resistance to swelling in the presence of printing inks containing ester solvents or UV-curable components.