The aim of the article is to study and develop welding numerical models in the phase transformation and damage condition. The models are based on the study of damage concept in the multiphasic behavior, which occurs by welding process. The core of models or constitutive equations is the coupling between ductile damage, small strain elasticity, finite visco-plasticity and phase transformation. Based on the theory of thermodynamics and continuum damage mechanics (CDM), constitutive equations are built to describe damage growth and crack appearance during and after welding. The thermodynamics of irreversible processes with state variables is used as a framework to develop the phase coupling model. The related numerical aspects concern both the local integration scheme of the constitutive equations and the global resolution strategies. In this study, the majority of efforts are devoted to the theoretical developing of damage model. In addition, the models are implemented in computing software MATLAB® and CEA CAST3M® finite element code, and some calculations are presented to further explain the models in the end of the article.