Wire electric discharge machining (WEDM) is a thermo-electric spark erosion non-traditional type manufacturing process. The applications of WEDM have been found in aerospace and die manufacturing industries, where precise dimensions were the prime objective. This process is applied in case of processing difficult to machine material. Brass wire is used as an electrode and High strength low alloy (HSLA) steel as a work-piece during experimentation. The present research deals with the effect of process parameters on the overcut while machining the HSLA steel on WEDM. The mathematical model has been developed with the help of Response Surface Methodology (RSM). Further this model is processed with help of Genetic Algorithm (GA) to find out the optimum machining parameters. The percentage error between the predicted and experimental values lies in the range of ±10%, which indicates that the developed model can be utilized to predict the overcut values. The experimental plan was executed according to central composite design. The optimal setting of process parameters is pulse on-time-117 μs; pulse off-time-50 μs; spark gap voltage-49 V; peak current-180 A and wire tension-6 g; for minimum overcut, whereas at the optimal setting overcut is 9.9922 μm.