Inconel 718 is a nickel-based alloy designed for high yield, tensile, and creep-rupture properties. This alloy has been widely used in jet engines and high-speed airframe parts in aeronautic application. In this study, electric discharge machining (EDM) process was used for machining commercially available Inconel 718. A copper electrode with 99.9% purity having tubular cross section was employed to machine holes of 20 mm height and 12 mm diameter on Inconel 718 workpieces. Experiments were planned using response surface methodology (RSM). Effects of five major process parameters—pulse current, duty factor, sensitivity control, gap control, and flushing pressure on the process responses—material removal rate (MRR) and surface roughness (SR) have been discussed. Mathematical models for MRR and SR have been developed using analysis of variance. Influences of process parameters on tool wear and tool geometry have been presented with the help of scanning electron microscope (SEM) micrographs. Analysis shows significant interaction effect of pulse current and duty factor on MRR yielding a wide range from 14.4 to 22.6 mm3/min, while pulse current remains the most contributing factor with approximate changes in the MRR and SR of 48 and 37%, respectively, corresponding to the extreme values considered. Interactions of duty factor and flushing pressure yield a minimum surface roughness of 6.2 μm. The thickness of the sputtered layer and the crack length were found to be functions of pulse current. The hollow tool gets worn out on both the outer and the inner edges owing to spark erosion as well as abrasion due to flow of debris.