This work introduces a new electrode geometry for making holes with high aspect ratios on AISI 304 using an electrical discharge drilling (EDD) process. In addition to commercially available cylindrical hollow electrodes, an elliptical electrode geometry has been designed, manufactured, and implemented. The principal aim was to improve the removal of debris formed during the erosion process that adversely affects the aspect ratio, dimensional accuracy, and surface integrity. The results were compared and discussed to evaluate the effectiveness of electrode geometry on the machining performance of EDD process with respect to the material removal rate (MRR,) the electrode wear rate (EWR), and the tool wear ratio (TWR). Dimensional features and surface characteristics of the drilled holes were also evaluated in aspects of overcut (OC), aspect ratio (AR), and surface roughness (SR). The experimental results revealed that an elliptical electrode is preferable for producing holes with good dimensional accuracy and improved surface quality. In addition, 3D models of flow field with liquid, gas, and solid phases are proposed for analyses of the interelectrode gap within the machining zone. Based on the results obtained from models, the elliptical electrode also exhibited good flushing capability for effective debris removal.