WEDM (Wire electrical discharge machining) has Amazon enhanced the deal with of modern and very rigid materials, specifically used for the medical industries, nuclear as well as aerospace. It is the most important Nontraditional machining procedure that is widely utilize for materials of machining difficult-to-machine like titanium, zirconium, etc., with complex aspect. Using numerical control WEDM, complicated profiles can be easily machined by electrically conductive materials of difficult-to- machine. The accuracy rate obtained along with the fine surface quality make the WEDM a much respected technology in the modern day manufacture. EN-31 alloy steel, widely used in automotive and lock industries, is electrically machined in order to study the effects of some important cutting parameters on MRR (Metal Removal Rate), Ra (Surface Roughness), and Overcut. Whereas the Metal Removal Rate determines the machining economics as well as production rate, the Surface Roughness (Ra) and Overcut denotes the quality of machining and degree of precision respectively. The experimental work during the study has been conducted on an ELECTRONICA SPRINTCUT WEDM machine and deals with the features of rough cutting regime of EN-31 alloy steel. The present work also highlights the growth of mathematical models for correlating the inter-relationships of different WEDM machining factors like; Surface roughness, MRR, P (water pressure), T (wire tension), F (wire feed rate), Ip (pulse peak current), Ton (pulse on-time) and Overcut while machining EN-31 steel. A second-order polynomial, such as machining parameters, has been established for MRR, Ra and Overcut with use of RSM (Response Surface Methodology). These models are established by conducting a designed experiment which was based on the RCCD (Rotatable Central Composite Design). Mathematical models that was fitted to the experimental data basically will be contributing to the optimization of process parameters.