A complete modeling of heat and fluid flow applied to laser welding regimes is proposed. This model has been developed using only a graphical user interface of a finite element commercial code and can be easily usable in industrial R&D environments. The model takes into account the three phases of the matter: the vaporized metal, the liquid phase, and the solid base. The liquid/vapor interface is tracked using the Level-Set method. To model the energy deposition, a new approach is proposed which consists of treating laser under its wave form by solving Maxwell's equations. All these physics are coupled and solved simultaneously in Comsol Multyphysics®. The simulations show keyhole oscillations and the formation of porosity. A comparison of melt pool shapes evolution calculated from the simulations and experimental macrographs shows good correlation. Finally, the results of a three-dimensional simulation of a laser welding process are presented. The well-known phenomenon of humping is clearly shown by the model.