Wire cut EDM (WEDM) is a thermo electric nontraditional manufacturing process in which material is removed by localized heating and melting. It is discrete spark generation method applicable for hard and difficult to machine materials. In this paper mathematical model developed for EN19 material with Stastical analysis software. Experiments are carried out using L27 Orthogonal array by varying Material Thickness, pulse on time, Pulse Off time, Flushing Pressure, Wire Tension and Servo voltage. Analysis found that varying parameters are affected for consumable wire with constant wire feed in different way for different response. Attempt to compare different order mathematical model for accurate modeling done in this research. Higher order mathematical model developed with R 2 value 0.9863 for MRR and 0.9918 for Surface roughness obtained which gives more accurate output for given input parameters. Keywords-WEDM, PULSE ON TIME, PULSE OFF TIME , MRR, REGRESSION I. INTRODUCTION WEDM is a non conventional thermo electric material removal method for conductive materials to cut intricate shapes and profiles with a thin wire electrode. The electrode is a thin wire of a diameter 0.05 to 0.25 mm copper or brass coated with mo lybdenum. As wire feeds fro m reel to reel, material is eroded fro m work material by a series of discrete sparks occurring between the work p iece and the wire under the presence of dielectric fluid which is continuously fed to the mach ining zone (1). The WEDM process makes use of electrical energy generating a channel of plasma between the cathode and anode (2) and turns it into thermal energy at a temperature in the range of 8000-12,000 oC (3). When the pulsating direct current power supply occurring between 20,000 and 30,000 Hz is turned off, the plasma channel breaks down. This causes a sudden reduction in temperature allowing circulat ing dielectric fluid to implore plas ma channel and flush mo lten particles fro m the pole surfaces in fo rm of microscopic debris (4).Erosion of metals by spark was first reported by Joseph Priesily in 1978, however controlled machining by sparks was first introduced by Lazarenko in Russia in 1944. The first Britis h patent was granted to Rudorff in 1950 (5). In 1974 D.H. Dulebohn applied optical-line follower system to auto matically control shape of component to be machined by W EDM proc ess. By 1975, its popularity was rapidly increasing, as the process and its capabilities were better understood by the industry. II. MATHEMATICAL MODELING Regression analysis is used to investigate and model the relat ionship between a response variable and one or more predictors. The term mu ltip le regression literally means stepping back toward the average. It was used by British mathematician Sir Francis Galton. Regression analysis is a mathematical measure of the average relationship between two or more variables in terms of the orig inal units of the data. In regression analysis there are two types of variables. The value whose value is influenced or is to be predicted is called dependent variable and the variable which influences the values or is to be used for prediction is called independent variable. Regression analysis can be done in two ways; A. Bivariate regression B. Multi ple regression a) Bivariate regression Two variables X and Y may be related to each other or inexactly. In physical sciences, variab les frequently have an exact relationship to each other. The simp lest relationship can be expressed by Y=a+Bx Where the values of the coefficient, a and b, determine respectively the p recise height and steepness of the line. Thus coefficient a represent to as the intercept or constant, and coefficient b referred to as the slope. In contrast, relationship between variables in social sciences is almost always inexact. The equation for a linear relationship between two social science variables would be written as: Y=a+bX+e , Where e represents the presence of error. b) Multiple regression analysis Multiple regression analysis is use when more than two parameters are used. In this research work, six control parameters were used. For mu ltip le reg ression analysis various types of modeling tool used as shown in fig