We present computer modeling along with experimental data on the formation of sharp conical tips on silicon-based three-layer structures that consist of a single-crystal Si layer on a 1μm layer of silica on a bulk Si substrate. The upper Si layers with thicknesses in the range of 0.8-4.1μm were irradiated by single pulses from a KrF excimer laser focused onto a spot several micrometers in diameter. The computer simulation includes two-dimensional time-dependent heat transfer and phase transformations in Si films that result from the laser irradiation (the Stefan problem). After the laser pulse, the molten material self-cools and resolidifies, forming a sharp conical structure, the height of which can exceed 1μm depending on the irradiation conditions. We also performed computer simulations for experiments involving single-pulse irradiation of bulk silicon, reported by other groups. We discuss conditions under which different types of structures (cones versus hollows) emerge. We confirm a correlation between the presence of the lateral resolidification condition after the laser pulse and the presence of conical structures on a solidified surface.