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The present research work mainly emphases on experimentation, analysis and optimization of machining parameters during WEDM on Inconel 825. Based on Box-Behenken Design, 29 experimental runs were executed on WEDM using 0.25 mm dia half hard brass wire and de-ionized water as dielectric. Controllable parameters pulse on time (Ton), pulse off time (Toff), spark gap voltage (SV) and wire feed (WF) are varied up to three levels to study their influence on response measures cutting speed (CS) and gap current (Ig). Experimental models were developed by employing RSM. Design expert software 7.0.0 was considered for design of experiments and developing the mathematical model. Graphical model analysis has been done with the help of Analysis of Variance (ANOVA). Ton, Toff and SV have major influencing factors on responses where, as wire Feed was insignificant. To achieve optimal parameter combination, multi-objective optimization of responses is performed using desirability method. Confirmation test is performed at optimal combination of parameters provided by desirability function to validate the study. Hence, predicted value lies in correspondence with the experimental findings.