Abstract: To understand the basic mechanism in the design and manufacture of welded structures, the evolution of stress and strain in the thermal-mechanical coupling process was studied by using one-dimensional bar model with rigid constraints on both ends. The necessary condition for the compressive plastic zones was proposed, namely, the temperature differences should no less than 2ΔT. Under force and moment equilibrium condition, the 1-Bar theory was applied into two-dimensional plates. The 3-Bar model was then developed to study the effects of welding heating and cooling processes on the distribution of two-dimensional longitudinal residual stress. It was found that the width of the local heated strip in 3-Bar model equals to the width of the welding plastic zone. The longitudinal residual stress of the welding plastic zone is close to the material yield strength. The dimension, profile and location of the plastic zone are the key parameters in the design of the weld joint. The asymmetric distribution of the neutral axis should be limited to avoid additional deformations. Flame straightening process was studied using 1-Bar model. It was found that the residual stress and the plastic strain could not be changed from the second thermal cycle. The repeated heating in the repair zone is useless. The effects of flame straightening could be predicted simply by inputting the heating peak temperature and heating width into 3-Bar model.