Tungsten Inert Gas (TIG) weld quality and mechanical properties are systematically structured by the bead width, reinforcement and penetration size. This study has developed a mathematical model using the second order quadratic polynomial model to select the best setting for the process parameters to produce the maximum penetration area in TIG welding.The set of experiment samples was produced from mild steel plates guided by a central composite design experimental plan. The results obtained revealed that the second order quadratic polynomial equation is the best fit model that can accurately explain the relationship between the input and the output parameters. The results possessed good statistical sufficiency, having a very good strength for predicting the target response. The prediction strength and models reliability factor are in reasonable agreement with each other, the surface plots showed the combined interaction of input parameters on the response, and the ANOVA results revealed that the penetration area is very sensitive to the current parameter. The mathematical models developed have a high goodness of fit, adequate signal,strength which can explain and predict the penetration area

Keywords : penetration area, models, Response Surface Methodology,, Tungsten Inert Gas, Welding,quality