The invention relates to a precision process, wherein a radical reaction of a radical produced from a gas on discharge or laser beam excitation in a gaseous atmosphere with an atom or molecule constituting a workpiece is utilized, a compound produced according to the reaction is vaporized and removed, and thus a workpiece such as silicon single crystal, ceramics material or the like can be smoothed, cut, bored, grooved and so forth without leaving a residual defect such as residual crack, thermally affected layer of the like on the surface.