Sheet-like reinforced materials consisting ofA. a core layer comprising a sheet-like textile structure, preferably a glass fiber mat,B. a plastic matrix composed of a nylon which has been polymerized under alkaline conditions and penetrates both the core layer and the surface layer of layers,are produced batchwise by the RIM method or continuously on a double-belt press by impregnating the sheet-line textile structure and the foam sheets with a lactam melt and polymerizing the latter. The reinforced material can be used for the production of finished articles having a satisfactory surface, for example for the automotive or aircraft industry.