There are several driving forces such as surface tension, buoyancy force, arc pressure, electromagnetic force, recoil pressure, drag force, etc. in gas tungsten arc (GTA) welding and laser welding, which have different influences on flow dynamics in the weld pool. This paper investigates the influence of respective driving forces on weld pool dynamics by using mathematical models and numerical simulations. In numerical simulations, the flow patterns in the weld pool and the maximum fluid velocity caused by respective driving forces can be observed, since driving forces can be applied separately. As all driving forces are applied under experimental conditions, the results of experiments and numerical simulations were compared to validate the numerical simulations and mathematical models used in this paper. In GTA welding, Marangoni flow can be considered as the most dominant force in the radial direction, while the velocity magnitudes of the z-axis direction of all respective forces except buoyancy and drag force are almost the same. The influence of buoyancy force is negligible. In keyhole laser welding, however, recoil pressure can be considered the dominant force, while the other driving forces have only a negligible influence on fluid dynamics in deep keyhole welding. In laser-GTA hybrid welding, recoil pressure can be considered the dominant force.