crest of a corrugation which is to be ground and the spring member 12 ill be permitted to relax adjacent to a valley the action of the spring members 12 may selectively be suppressed in that each spring member 12 is bridged by a rigid support 13 which is non displaceably connected by a tubular member 14 to the guide yoke 6 in which the abrasive product 3 is movably mounted that rigid support 13 co operates with a hydraulically operable supporting cylinder 15 which either releases the support 13 or constitutes for that support an abutment which can be adjusted in height and which will then prevent a vertical movement of the guide yoke 6 relative to the grinding frame 7 owing to the wear of the abrasive product 3 its circumferential surface will be adapted to the profile of the top surface 1 of the rail 2 after a short grinding time to permit a grinding of the top surface 1 to a predetermined profiled shape the abrasive product will have to be dressed accordingly for this purpose rotating dressing members 16 are provided which are shown in fig6 and are freely rotatably mounted in a bearing yoke 17 and by means of the bearing yoke 17 can be moved against the associated abrasive product 3 in a radial direction with respect to the abrasive.