This article presents the identification of the influence of the effects and interactions of the machining parameters (EDM) of the machine (EROTECH basic 450) in order to model the material removal rate (MRR), the tool wear rate (TWR) and the roughness of the part (Ra). We look at all the machining parameters and collect the effects by the design of experiments method. The modeling carried out is thus carried out by the response surfaces method (RSM). We use the statistical method (ANOVA) analysis of variance to approve the robustness of the models and to verify that they are statistically significant. The Taguchi method was implemented to formulate mathematical models to predict EDM machining parameters. The prediction of responses by empirical models is compared with experimental validation tests and the results are satisfactory.