Magneto-caloric materials such as Beryllium, Gallium, Cadmium and Tungsten are most suitable for regulating the heat flow at a cryogenic temperature below 10 K. Among these, Tungsten is preferable as a switching element in magnetoresistive heat switches because of its high Debye temperature and low critical superconducting temperature. Machining tungsten is difficult because of its inherent properties. Due to this, WIRE Electrical Discharge Machining (WEDM) process is preferable to convert tungsten into the desired shape and size. Thus, current research has focused on the WEDM process. Before machining of material, parametric optimization is needed to reduce the operating cost, material wastage, number of experiments and time. Therefore, the present research has focused on optimizing the process parameters using the Taguchi Grey Analysis (TGA) method for the WEDM process of tungsten. In this method, seven input parameters such as pulse on, pulse off time, arc off time, water pressure, wire feed, wire tension, gap voltage, and three output parameters, such as material removal rate (MRR), Kerf width and surface roughness value, are chosen for parametric optimization. The parametric optimization study of machining single-crystal pure tungsten using WEDM signifies that the response parameters should (MRR is 0.298 mm(3)/min, Kerf width is 0.346 mm, Surface roughness is 1.834 & mu;m).