In the present work, a thermal-structural model is presented to analyze the process parameters and their effect on three important responses such as material removal rate, tool wear rate and residual stresses on work piece in electrical discharge machining (EDM) process. The numerical model is validated conducting experiments on a die-sinking EDM machine. The numerical method provides an inexpensive and time saving alternative to study the performance of machining before actual cutting operation. A Box-Behnkin design of response surface methodology is adopted to collect data for analysis. Regression analysis is conducted to develop equations relating responses with process parameters. Finally, non-dominated sorting genetic algorithm is used to obtain pareto optimal solution for multi objective optimization