WEDM is used chiefly for machining Titanium and its alloys with good dimensional accuracy and surface finish. The research work has been done with the BBD of the RSM technique, and further multi-response optimization was done through the desirability function. The results of the research work shows that the effect of input variables pulse on-time (POT), pulse off-time (POFT,) spark gap voltage (SGV), and concave profile radius (CPR) on the output variables surface roughness (SR), and geometric error (GE) have been investigated. It observed that POT is the primary significant factor affecting the SR, and GE. With increases in CPR, Geometric error also increases. CPR is the most critical factor for the geometric error, with an 82.83% contribution. Experiment results also shows that POT and POFT significantly affected the surface integrity with the formation of pockmarks, overlapping craters, micro-cracks, and recast layer.WEDM is used chiefly for machining Titanium and its alloys with good dimensional accuracy and surface finish. The research work has been done with the BBD of the RSM technique, and further multi-response optimization was done through the desirability function. The results of the research work shows that the effect of input variables pulse on-time (POT), pulse off-time (POFT,) spark gap voltage (SGV), and concave profile radius (CPR) on the output variables surface roughness (SR), and geometric error (GE) have been investigated. It observed that POT is the primary significant factor affecting the SR, and GE. With increases in CPR, Geometric error also increases. CPR is the most critical factor for the geometric error, with an 82.83% contribution. Experiment results also shows that POT and POFT significantly affected the surface integrity with the formation of pockmarks, overlapping craters, micro-cracks, and recast layer.