SS 304L is an austenitic Chromium-Nickel stainless steel offering the optimum combination of corrosion resistance, strength and ductility. These attributes make it a favorite for many mechanical components. The paper focuses on developing mathematical model to predict ultimate tensile strength of pulsed current micro plasma arc welded SS304L joints. Four factors, five level, central composite rotatable design matrix is used to optimize the number of experiments. The mathematical model has been developed by response surface method and its adequacy is checked by ANOVA technique. By using the developed mathematical model, ultimate tensile strength of the weld joints can be predicted with 99% confidence level. Contour plots are drawn to study the interaction effect of welding parameters on ultimate tensile strength of SS304L weld joints. The developed mathematical model has been optimized using Hooke and Jeeves Method to maximize the ultimate tensile strength.Keywords. Pulsed current micro plasma arc welding, SS304L, ultimate tensile strength, design of experiments, ANOVA , Hooke and Jeeves algorithm.