The present research work is concentrated around the machining of titanium grade 5 alloy using electric discharge drilling. The process response parameters viz. hole taper and hole dilation have been calculated by performing experiments. During the experiments titanium grade 5 alloy has been taken as a workpiece with brass electrode as a tool. The experimentally calculated process parameters have been optimized using grey relational analysis. The main objective of this research is to maximize the hole circularity along with minimum hole taper and dilation by selecting the optimal input parameters. From the results it has been found that discharge current is the most effective parameter for the given conditions.