Abstract: A crankshaft having a substantially cylindrical crank surface centered on a crank axis and a pair of axially confronting and axially spaced cheek surfaces flanking the crank surface and meeting the crank surface at respective fillets is ground by an apparatus having a shoe between the cheek surfaces and having an end directed at the crank surface and sides directed at and spaced inward from the cheek surfaces. A pair of side parts on the sides of the shoe each can move axially of the shoe relative to the crank axis and a flexible grinding band is stretched over the side parts and shoe. The crankshaft is rotated about the crank axis or an axis parallel thereto and the shoe is urged radially toward the crank axis to press the band against the crank surface. The crankshaft and the shoe between the cheek surfaces are relatively axially reciprocated and each of the side parts is urged axially outward away from the shoe to press the band axially against the cheek surfaces.