An assembly for securing at least one rail to a substrate has a longitudinally extending rail plate extending across and secured underneath the rail and having a pair of opposite ends. Respective end restraints at the ends of the rail plate each have a jaw fixed to the respective end of the rail plate and each formed with a vertically throughgoing passage. A respective rigid anchor hood is fixed to the substrate in each of the passages with an outer surface of the anchor hood spaced inward from an inner surface of the respective passage and forming an annular space therewith. A respective rubber bumper mass fills each of these spaces so that forces transverse to the rail are transmitted through the bumpers to the anchor hoods.