PURPOSE: To make a cavity carrying a thread groove formable easily and yet accourately, by using a tool electrode in specified form, while operating for electric discharge machining with this electrode moved for the top of a piston through the feed per stroke and the extent of rotation in a proper manner.

CONSTITUTION: In time of EDM operation, first a piston 7, which preforms a circular hole 13 with proper depth in its top part, is set on a setting table 11 inside a vessel 4 holding oil. Next, this oil inside the vessel 4 is circulated around therein whereby shifted into an EDM process but this process is constituted of the following stages of work that 1) a non-machining process in which a tool electrode 1 having a squarelike plate part 102 is fed in a direction H, making it do non-machining, and oppositely installed in a piston top surface 701 via a discharge clearance, then actual electric discharge machining is started and 2) a drilling process in which the tool electrode 1 is shifted into movement along each pattern of the feed per stroke S and the extent of rotation θ, and then drilling takes place whereby a cavity 12 is formed up. And, with this operation, a thread groove B being cut in a peripheral edge part of the plate part 102 is formed on an inner wall surface of the cavity 12.