A mathematical model is developed for the simulation of keyhole and molten pool formation during laser beam welding. Heat transfer from the key hole to the weld pool and details of the fluid flow play a major role in determining the weld bead profile. The simulation is performed based on the control volume method (CVM) and a volumetric heat source is used to model the laser beam and the equations of mass, momentum and energy are solved. The effect of Peclet number, Marangoni number, and Nusselt number is studied by varying process parameters like welding speed and beam power. The simulated bead profiles are compared with the experimental profile and are found to be acceptable.