Abstract: The machine comprises at least one workpiece-bearing device is provided, upon which a tile or a stack thereof can be placed and blocked. The workpiece-bearing device is revolvable and can be positioned at any angle about a fixed axis. At least one drive head is fitted with at least one rotating grinding wheel, which operates on one side of the tile or on same sides of tiles forming the stack. The workpiece-bearing device and the drive head are constrained to a fixed frame in such a way that a plane of work motion of the at least one grinding wheel is disposed parallel to an axis of rotation of the workpiece-bearing device.