The effect of different shapes of laser beam power density distribution was investigated numerically with respect to the thermo-hydrodynamics of the melt pool during welding. The process addressed is conduction mode bead on plate welding of the Titanium alloy Ti-6Al-4V. A new solver based on the volume of fluid method to track the deformation of the melt free surface was developed in the OpenFOAM software. Experiments were conducted for the purpose of validating the model. In addition to the traditional cross-cut images of the weld bead, top view images of the melt pool were analysed to perform the validation along the 3-space dimensions. A good agreement between numerical predictions and experimental measurements was obtained, thus promising aconfident utilization of this simulation model when investigating the influence of beam shapes on the resulting weld seam. The effectof three different beam shapes on the melt pool velocity flow, temperature fields, and melt geometry were studied. It was found that the melt pool size was largest for an elliptical power density distribution with the major axis along the welding direction. The results also showed that the laser beam with Gaussian power density distribution resulted in the deepest penetration.