The use of electromagnetic force to stir molten metal in some casting processes was reported long ago. Recently, it has been demonstrated that by applying an external magnetic field along with or without an external electric current, the melt flow in the weld pool can be influenced leading to the change of weld shape in both CO2 and Nd:YAG welding of aluminium alloys with or without filler metal. However, so far these very limited studies are based on experiments and no theoretical explanations are given. Hence, there is a strong need to fundamentally understand how the electromagnetic force is affecting the melt flow and the resulting weld pool shape. This would provide a foundation to optimize and control process parameters in order to achieve the desired weld pool shape. In this paper, mathematical models and the associated numerical techniques have been developed to systematically investigate the effects of electromagnetic force in laser keyhole welding. The transient weld pool fluid flow and the shape of the solidified weld are calculated under various electromagnetic conditions for both spot and 3-D moving laser welding. The parameters studied include the magnitude, duration, and direction of the electrometric force, welding speed, and the time when electromagnetic force is applied, etc. In addition, the feasibilities of using electromagnetic force to eliminate porosity formation and to modify weld bead surface smoothness are conducted. Computer animations showing the fluid flow and weld pool dynamics, and how the electromagnetic force influences the melt flow behaviors will be shown in the presentation.