A rail fastening arrangement in which a rail for a rail vehicle is fastened to a base, and to a shim. The rail fastening arrangement includes two guide plates, of which one guide plate respectively is associated with one of the longitudinal sides of the rail, and a shim which is arranged between the base and the rail. The shim, at its top, has a contact area on which the rail is supported, and, at its bottom, has a supporting surface by way of which the shim is supported on the base. The contact area and the supporting surface of the shim, viewed in a section located transversely to the longitudinal extension of the rail, enclose an acute angle. The edge at which the shim is thinner is arranged beneath the rail, fastening of rails oriented at a cant relative to the vertical in the region of points.