Steady state and transient laser melting problems are numerically simulated. Enthalpy formulation is used for solving the energy equation and momentum equations are solved only in the liquid domain by the SIMPLE algorith. Using a Gaussian distribution of input heat flux, a wide range of studies are performed for steel and aluminium by varying the beam power density and the beam radius. The pool shape and the surface tension driven flow field are found to be quite different in nature for steel and aluminium. The streamline plots show the existence of two contra-rotating cells in the molten pool the size and strength of which are found to be strongly dependent on the material property, i.e. the Prandtl number.