A numerical analysis of three-dimensional keyhole dynamics is accomplished for the laser drilling of 2mm thickness carbon steel. The molten and re-solidified free surface is tracked by the volume of fluid method. One of the important features, referred to as the multiple reflections of a laser beam in a keyhole, is implemented in real-time during the computation. Fresnel reflection theory is adopted to describe the energy absorption mechanism. In particular, the effect of polarization of the laser is investigated through the Fresnel reflection model. Analyses are carried out for both circularly and linearly polarized beams. The simulation results show that the keyhole under a circularly polarized laser is symmetric along the beam axis, while for the case of a linearly polarized beam the keyhole is asymmetric and is stretched along the direction of polarization.