Abstract: A cylindrical workpiece has an end face ground on two synchronously driven supporting rollers, by a grinding tool mounted on a drive shaft in front of the supporting rollers, and a loading mechanism and an unloading mechanism. The loading mechanism and the unloading mechanism are a simply functioning loading and unloading unit which has a carriage mounted above the supporting rollers limitedly slidable back and forth on an upright frame portion and two bent workpiece carriers supported on the upright frame portion pivotable about horizontal pivot axes. Each of the two bent workpiece carriers is pivotally connected by a link member to the carriage and has a working arm which is provided with a holder and with a pressing roller enclosed in the holder with a predetermined clearance. The bent workpiece carriers are pivotable with the back and forth motion of the carriage so that the working arms alternatingly pivot between a grinding position and a loading and unloading position.