The aim of this work is to study the effects of several wire electrical discharge machining (WEDM) process parameters, such as the servo voltage (SV), the pulse on time (TON), and the pulse off time (TOFF) on the surface finish (SR) and the kerf width (KW) of stainless steel 304 as a workpiece material. A multi-responses optimization approach based on Grey relational analysis has been designed, and it was discovered that the main affecting factor is the pulse on time followed by the servo voltage. According to the data, the grey relation analysis (GRA) grade for the second trial, including (a servo voltage of 14V, a pulse on time of 100µs, and a pulse off time of 45µs), was the optimum combination of settings that may concurrently optimize all of the specified response qualities. By utilizing the regression analysis, the mathematical equations illustrating the link between the input parameters and the responses have been established. In particular, the findings of this article will assist manufacturing engineers in selecting an optimal set of process parameters for machining stainless steel (SS304) grade.