The rapid melting of a semi- infinite body due to the absorption of a CW laser beam radiation has been studied. The enthalpy technique for the solution of phase change problems has been used in an explicit finite difference form to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. The technique has been modified so that it is not necessary to assign a constant temperature, Tm, to the mesh element that contains the melt front. Instead, a new value of temperature is calculated for the grid point at each time step by incorporating the energy boundary condition at the solid- liquid interface. Calculations have been carried out for laser beam with circular and elliptical profile and for a range of material translational speeds. The numerical results were compared with the experimental data. Increasing the translational speed causes the heat affected zone and the size and shape of melt pool to become smaller.