Abstract: A grinding stone for grinding a railhead surface of a rail includes abrasive material. The abrasive material has a first side surface and an opposed second side surface. The first and second sides surfaces are joined by a circumferential surface. The circumferential surface is transversely disposed with respect to at least the first side surface. The abrasive material presents a bevelled grinding surface extending from a substantially circular locus of points on the second side surface to a substantially circumferential locus of points on the circumferential surface. A method of re-profiling the railhead surface of a rail includes the steps of:rotating at least one grinding stone;bringing the bevelled grinding surface of the grinding stone into contact with the railhead surface; andadvancing the grinding stone along the rail.