A grinding machine for the rolls of a roll stand includes a guide unit extending parallel to the roll to be ground. Mounted on the guide unit is a grinding unit which is displaceable in longitudinal direction of the roll by a displacement drive. The grinding unit is adjustable relative to the roll by adjusting drives. The guide unit is provided with a rotary drive which is capable of rotating the guide unit about its longitudinal axis. The grinding unit is formed by a grinding element which is symmetrical with respect to rotation. The grinding element is connected to the guide unit in such a way that the grinding element and the guide unit rotate together.
