A grinding method and to a cylindrical grinding machine grinds metal rod that is pushed through a chuck of a workpiece spindle head. Two backrest seats are ground on and two backrests are then seated. The support of an end area enables a front cone to be ground. A grinding wheel comprised of two different individual wheels serves to grind the front cone and is advanced toward the round rod in the X-direction. The front cone is lodged in a hollow punch at a front end of a quill by displacement of the quill. The desired cylindrical grinding a final contour of the end area is done. Working the rod is done with a single chucking and the end area is cut off from the round rod by one of the individual wheels.