Many welded structures are fabricated from stainless steels because these steels have good mechanical properties and good corrosion resistance. It is necessary to predict the residual stress after welding in order to evaluate the performance of the welded joint. In this paper, the butt welded joint of AISI 316L stainless steel plates is studied. The Metal Inert Gas (MIG) welding process is selected for this material. A SYSWELD software based on the Finite Element Method (FEM) is used to determine the temperature field and residual stresses of two stainless steel plates. The welding simulation includes a sequential coupled thermomechanical analysis. The elemental generation and death technique is utilized to simulate metal deposition in welding. The double ellipsoidal heat source model is used for the heat input of the MIG welding process. The temperature distribution for various time steps at some important points is presented. Cooling times and cooling rates over a temperature range of 800 oC to 500 oC at these points are determined. The residual stress distribution in the longitudinal and transverse direction in two cases with and without clamping is obtained and compared. Obtained results show that: the temperature field in the case of clamping is the same as in the case of no clamping; only the longitudinal stress and transverse stress components are important, the other stress components are not important; the longitudinal stress at the middle of weld line is very high; the transverse stress in the case of clamping is greatly increased, so it is necessary to limit clamping to reduce residual stress after welding