We present analytical and computer modeling along with an experiment on the formation of sharp conical tips on monocrystalline silicon thin films, silicon-on-insulator, subjected to irradiation by single 25 ns pulses from a KrF excimer laser focused into a spot several micrometers in diameter. These fabricated structures have heights of about 1 μm and apical radii of curvature of several tens of nanometers. We offer a simplified analytical model for the formation of these structures. The computer simulation includes two-dimensional time-dependant heat transfer and phase transformations in Si films on SiO2 substrates that result from the laser irradiation (the Stefan problem). It is shown that upon irradiation and initial melting, the liquid/solid interface remains mainly parallel to the surface of the film. After the laser pulse, the molten material self-cools and resolidifies. The solid/liquid interface moves predominately laterally toward the center of the irradiated spot, forming an almost vertical front. We discuss the relation between the dynamics of the melting/freezing front movement and the displacement of material in the irradiated spot.