Wire electrical discharge machining (WEDM) has tremendously improved the processing of newer and very hard materials, especially used for the aerospace, nuclear, and medical industries. It is the most important Nontraditional machining process which is widely used for machining difficult-to-machine materials like titanium, nimonics, zirconium, etc., with intricate shapes. Using numerical control WEDM, complicated profiles can be easily machined through difficult-to-machine electrically conductive materials. The high degree of accuracy obtained and the fine surface quality make WEDM a very valuable 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 Metal Removal Rate (MRR), Surface Roughness (Ra), and Overcut. Whereas the Metal Removal Rate determines the economics of machining and rate of production, the Surface Roughness 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 development of mathematical models for correlating the inter-relationships of various WEDM machining parameters such as; pulse on- time (Ton), pulse peak current (Ip), wire tension (T), wire feed rate (F) and water pressure (P) on Metal removal rate, Surface roughness and Overcut while machining EN-31 steel. A second-order polynomial, in terms of machining parameters, was developed for Metal removal rate, Surface roughness and Overcut using Response Surface Methodology (RSM). These models are developed by conducting a designed experiment based on the Rotatable Central Composite Design (RCCD). Mathematical models fitted to the experimental data will contribute towards optimization of process parameters.