Welding distortion is more serious problem than any other problems caused by welding process, especially, in the heavy-industrial place. These welding distortions are caused by nonuniform heating and cooling of metal during and after welding operations. And these distortion quantities are must be known to worker in production line because distorions are important role in assembling part. Therefore an analytical model to explain and predict the welding distortion are needed. A numerical analysis of welding distortion which is inelastic behavior of weldment would require the three dimensional calculation. But computing time and memory would be very large, and the resulting cost might be unacceptable. Therefore we use a numerical technique for two dimensional analysis in the section normal to the weld direction of weldment under an assumption of quasi-stationary conditions. But the result of the calculation under two dimensional(plane strain) assumption was not satisfied as compared with experimental result. This paper proposed a technique for analysing the welding angular distortion by using a constraint boundary condition on the two dimensional finite element model. The simulation results revealed that the constraint boundary model could more reasonably describe the welding distortion than the plane strain model did.