Surface structuring using nano-second lasers can be used to enhance certain properties of a material or even to introduce new ones. One way to create these structures efficiently is direct laser interference patterning using different polarization vector orientations of the interfering beams. However, experimentally measuring the fabrication process of these structures is very challenging due to small length and time scales. Therefore, a numerical model is developed and presented for resolving the physical effects during formation the predicting the resolidified surface structures. This three-dimensional, compressible computational fluid dynamics model considers the gas, liquid, and solid material phase and includes various physical effects, such as heating due to the laser beam for both parallel and radial polarization vector orientations, melting, solidification, and evaporation, Marangoni convection, and volumetric expansion. The numerical results reveal a very good qualitatively and quantitatively agreement with experimental reference data. Resolidified surface structures match both in overall shape as well as crater diameter and height, respectively. Furthermore, this model gives valuable insight on different quantities during the formation of these surface structures, such as velocity and temperature. In future, this model can be used to predict surface structures based on various process input parameters.