Wire arc additive manufacturing allows the production of metallic parts by the deposition of weld beads using arc-welding technologies. This low-cost additive manufacturing technology has the ability to manufacture large-scale parts at a high deposition rate. However, the quality of the obtained parts is greatly affected by the various thermal phenomena present during the manufacturing process. Numerical simulation remains an effective tool for studying such phenomena. In this paper, a new finite element method is proposed in order to model material deposition and heat input in WAAM process. This method allows to gradually construct the mesh representing the deposited zones along the deposition path. The heat source model from Goldak is adapted and combined with the proposed material deposition technique considering the power distribution between the filler material and the molten pool. The effectiveness of the new method is validated through a set of experimentations, one of which is detailed in this paper.