A system for fastening a rail on a substrate includes a base plate, molded into which is a central portion, the width of which is adapted to the width of the rail foot of the rail to be fastened, with at least one fastening element for connecting the base plate to the substrate. The at least one tensioning element is provided for holding down the rail on the base plate. The system provides a fastening system allowing fastening of rails that satisfies modern requirements with the additional benefit of low production costs and simple assembly, while maintaining the basic configuration of the base plate provided and using simple means.