Abstract: The calculating formulas of top and bottom pool-surface deformation in TIG full-penetration weld pool is developed based on principles of fluid mechanics and variation calculus. A mathematical model has been estabished for the fluid flow and heat transfer in TIG full-penetrated Weld pool.Difficulties associated with irregular shape of the deformed weld pool surface have been sucessfully overcome by calculating the surface deformation together with the fluid flow and heat transfer in weld pools. Data of fluid velocity and temperature distribution in weld pools are obtained, so do that of top and bottom pool-surface deformation. TIG welding experiments show that the predictions of the model have a good agreement with the experimental observation with respect to weld pool shape.