The growing demands for high surface finish with complex shape geometries, traditional machining is now being substituted by unconventional machining processes. Wire Electric Discharge Machining (Wire EDM) is one of the unconventional metal cutting processes. Stainless Steel 304 (SS 304) is widely used in Aerospace, Medical, Electronics and Semiconductor, Tool and Die making industries. However, during traditional machining of SS 304, industries are facing numerous difficulties. In view of the exceeding purposes and challenges in traditional machining of SS 304, the present research investigates the effect of Wire EDM parameters such as Current (I), Gap Voltage (V), Pulse on time (Ton), Pulse of time (Toff) with two different electrode wire materials (Brass and Zinc coated brass) on SS 304 material. After machining, Surface roughness (SR), microhardness (HV) of the machined surface and thickness of recast layer were measured to assess the machinability of the SS 304. Wire EDM experiments have been performed using a CNC Wire EDM machine as per Taguchi's L-18 orthogonal design. Coated and uncoated brass wires of. 0.2 mm were taken as wire electrode materials. From the study, coated brass wire has shown the high surface finish and hardness than uncoated brass wire. Furthermore, the recast layers of the machined surfaces were analyzed for both wire electrodes using the SEM images. Analysis of variance (ANOVA) was carried for finding significant parameter for all output responses. Finally, grey relational analysis (GRA) was applied to find overall optimized process parameter mixture for maximization of hardness and minimization of SR.