Abstract: There is disclosed a self-centering template useful for centering cylindrical bodies on their axes in rotating machines such as a concentric grinder. The centering templates of the invention are generically cup-shaped plates, having an end disc with a dependent, preferably integral, cylindrical wall. The disc has a central aperture which is intersected by a radial slot extending from the periphery of the disc. The inside surface of the annular wall is tapered from a maximum thickness adjacent the disc. In use, templates are placed over the opposite ends of a cropped silicon ingot and the resultant assembly is mounted in the concentric grinding machine, with the central aperture of the template disc guiding the head stock and tail stock chuck into centric engagement with the ends of the ingot. After the ingot is clamped in the machine, the templates are removed by passing the radial slots of the templates past the machine shafts.