Abstract: The principle of the stress-free welding with cold source or displacement-controled load was demonstrated by using one-dimensional rod model. The numerical simulation experiment was used to discuss the way to realize the welding method. The time history distributions of physical quantities such as stress and plastic strain at the center point of the bar under seven loading schemes were numerically simulated and compared in detail. It was considered that the welding residual stress would be zero when the mechanical strain generated by the external displacement-controled load and thermal input at any time satisfied certain conditions. The best residual stress reducing effect was obtained when the deformation rate produced by the process of reducing residual stress with welding is the same as that of thermal expansion or thermal shrinkage in the local area. Based on the principle derived from this model, the principles and parameter setting basis of process, such as pre-stretching, pre-welding thermal tensioning, dynamic thermal tensioning and low stress and non-deformation (LSND), were discussed. It is an effective way to reduce welding residual stress by generating a large enough tensile plastic strain when the weldment is cooled.