An EDM method of and apparatus for machining the surfaces of a cavity in an electrically conductive workpiece utilize an electrode assembly comprising a plurality of segmented electrodes having their respective machining surfaces which collectively form a contour corresponding in shape to the cavity and being supported so as to be spaced apart and movable relative to each other in the assembly. An EDM power supply is used to electrically energize the segmented electrodes individually with respect to the workpiece and a plurality of drive units are provided to individually displace the segmented electrodes, independent of one another, relative to the workpiece, along their respective predetermined paths of translational motion, thereby permitting electrical discharges to develop between each of the surfaces of the cavity and the machining surface of each of the segmented electrodes brought proximate thereto across a fluid-filled machining gap during the individual translational motion thereof.
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