In the fabrication of a poly-Si film, an a-Si thin layer on glass substrate is melted by the irradiation of an excimer laser with the duration of nanosecond scale, and then is cooled down to form the poly-Si one. For analyzing the fabricating process, an efficient two-dimensional numerical model has been developed in this work, based on the finite difference method and the specific heat/enthalpy method used to handle the release of latent heat. The model can simulate the heat transfer, melt and solidification behavors of a-Si films subjected to the laser irradiation. Numerical analysis was performed by solving the heat flow equation which incorporates the material properties of temperature dependence, the surface reflectivity of silicon film, the variation of the incident power density with time and heat lose by the radiation and convection from the film surfaces into the surroundings. From the analysis of temperature responses for different laser intensities, the thresholds corresponding to the surface and full melting of the Si film can be found. The temperature responses are essentially different in the partial-melting and the complete-melting regimes. The Ft (surface melting threshold) and Fc (full-melt threshold) obtained from the simulation results of the proposed model in this study agree fairly well with those from the experimental data reported in the literature. In the partial-melting regime, the maximum temperature is close to the melting point of amorphous Si, since it is the point where solid a-Si is transformed into liquid state and the high latent heat can absorb extra energy to keep the temperature at the melting point. The fluence larger than Fc is the complete-melting regime, the maximum temperature increases with fluence. It is also found that the variation of the surface reflectivity gives a good way to observe the phase change and the melting duration. When the a-Si melts, the reflectivity rapidly goes up to a steady value which is consistent with the reflectivity of liquid silicon, and stays there until the melt silicon begins to solidify. As the irradiation energy of laser increases, the melting duration in the silicon layer is prolonged.