An apparatus for machining a web-shaped workpiece includes a workpiece supply for supplying workpiece rolls each of an elongate thin metal sheet, a processing machine for machining the elongate thin metal sheet into caps, a workpiece feeder for feeding the elongate thin metal sheet to the processing machine, and a product feeder for automatically separating the caps from scrap and feeding the caps to a product collecting mechanism. The apparatus is capable of efficiently and quickly producing various products from the elongate thin metal sheet.