A method of and an apparatus for machining interfitting members to improve their fit wherein the members are positioned to place their surfaces to be interfitted in a complementary relationship with a small gap spacing therebetween. A fluid delivery assembly includes a manifold supplied with a pressurized EDM liquid medium from a source thereof and a plurality of nozzles having each a respective valve and commonly projecting from the manifold. The nozzles have their respective nozzle outlets arranged in an array so as to be disposed individually adjacent to and distributed uniformly in the array along a continuous opening or slit formed as a continuous, narrow and elongate outlet opening of the gap spacing between the members where the surfaces to be interfitted terminate. A control unit sequentially opens the valves in a predetermined order, determined according to a particular surface characteristic of the surfaces which impedes a desired interfit therebetween, to allow the pressurized liquid medium in the manifold to be delivered sequentially to flush therewith particular areas in the gap spacing from the corresponding nozzle outlets. An EDM system having an EDM power supply and a servo system for relatively advancing the members effects electrical discharges successively in the particular areas mentioned, to sequentially remove the surface characteristic until the surfaces establish the desired interfit.