For a better understanding of the physical phenomena associated with the appearance of defects in laser welding, a heat and fluid flow model is developed using Comsol Multiphysics®. This first step of the project is focused on the modeling of a static laser shot on a sample of steel. This 2D axially-symmetric configuration is used to study the main physical phenomena related to the creation of the keyhole. This model takes into account the three phases of the matter: the vaporized metal, the liquid phase and the solid base. To track the evolution of these three phases, coupled equations of energy and momentum are solved. The liquid/vapor interface is tracked using the Level-Set method. The calculated velocity and free surface deformation are analyzed. Melt pool shapes are compared with experimental macrographs and the influence of some parameters such as laser power is discussed.