Abstract: An automatic chamfering machine for ceramic honeycomb structural bodies and the like workpieces is disclosed, and includes a clamping device by which a workpiece is clamped and caused to rotate in one direction. The movement of a grinder wheel with respect to the workpiece is controlled by a tracer element urged against the other peripheral surface of the workpiece itself, so as to carry out an autoprofiling chamfering operation. The grinder wheel thus removes a constant amount of material from the workpiece even when the workpiece has an irregular outer contour, or is clamped inaccurately.