Abstract: Based on the theory of magneto-hydro dynamics and real welding conditions,a three-dimension united mathematical model of TIG welding arc and weld pool was established.This model avoided the assumption of constant conditions of interface between welding arc and pool,and made analysis on behavior of arc and pool more near to real situation.Fluid flow and heat transfer of TIG welding arc and pool were analyzed based on built model with finite element analysis method.Equivalent latent heat was adopted to determine liquid quantity and solid-liquid identity was adopted to solve moving interface between molten and solid region.Computational results of welding arc and pool were close to those of the experiments.