The invention seeks to provide a method of producing slices, such as semiconductor wafers, from a rod-like ingot, which does not require any cutting margin for slicing so that less material is consumed, and also is free from warping or denatured layer of the slices, as well as being free from operating environment deterioration with high quality. A cylindrical ingot is obtained by cutting or grinding the outer periphery of a rod-like ingot, and it is then formed with a plurality of annular grooves at a predetermined pitch in its longitudinal direction to obtain a cylindrical work with annular grooves. The work is then severed in the section defined by the bottom of each annular groove by generating a stress in excess of the rupture strength of the slice in the groove.After the heating of the cylindrical work with annular grooves, the under-process end face of the work is suitably cooled quickly by cooling water jet from a jet nozzle from the outer periphery toward the center of the work.