The objective of the present investigation is to find the optimal set of process parameters to achieve higher depth of penetration (DOP) in A-TIG welding of stainless steel (SS) alloy 304L. Input parameters selected for experiments were current, welding speed and arc gap and design of experiments was carried out using central composite design of response surface methodology. Autogenous bead on plate welds in the presence of mono-component flux were made on SS 304L plates of thickness 6 mm to generate data and to study the influence of input variables on DOP. ANOVA was carried out to determine the significance of the process parameters and it was found that welding current is the most significant input variable influencing DOP. A linear regression equation was developed to predict DOP for a given set of input process parameters. Then, desirability approach of RSM is used for numerical optimization to obtain maximum depth of penetration.