Present work proposes a thermo-numerical model for accurate prediction of material removal and tool erosion for electrical discharge machining (EDM) process. The data collected for the numerical analysis is based on Box-Behnken’s experimental design, a popular response surface methodology (RSM) approach. The numerical model is validated by comparing experimental results on a die sinking EDM machine. A sequentially coupled thermo-structural model has also been proposed to estimate the residual stress distribution on the work piece. Analysis of variance is conducted to identify significant parameters. Regression analysis is conducted on the model to develop valid mathematical models relating responses with process parameters. Finally, a multi objective particle swam (MOPSO) algorithm has been adopted for simultaneous optimization of responses. The proposed model can be employed for selecting ideal process states to improve process productivity and finishing capabilities. © Springer International Publishing Switzerland 2015.