Thermally imageable elements and methods for their preparation and use are disclosed. The elements contain, in order, a substrate; an underlayer; and an ink-repellent layer. The underlayer contains a crosslinked allyl functional polyurethane. A photothermal conversion material is present in either in the underlayer or in an absorber layer between the underlayer and the ink-repellent layer. Thermal imaging and development removes the ink-repellent layer and reveals the underlayer in the exposed regions to form an imaged element useful as a waterless lithographic printing plate.