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Titanium is slivery gray metal, ductile with 22th element in the model periodic table with atomic weight of 47.9 and density of 4.67g/cm3 which is between Aluminum and Iron. Titanium has another property like it is paramagnetic in nature, high melting point and boing point near about 1668°C (3034°F, 1941K) and 3287°C (5948°F, 3560K) which make it to heat resistance. With most demanding properties of titanium material like highly strength/weight ratio, anti-corrosivity properties which makes it difficult to machining by conventional methods. WEDM is mostly used for machining the Titanium and its alloys with good accuracy of dimensional and surface finished. The research work has been done with the Box-Behnken design of RSM technique and, the multi-response optimization was done through desirability function. Result of research work shows that effect of input variables POT, POFT, SGV, and concave profile radius on the output variables cutting speed, surface roughness, and geometricerror. Experiment results shows that POT is the major significant factor that affect the cutting speed, surface roughness and also geometric error.