The Stefan problem in a semi-infinite media under laser irradiation is considered, which is related to the melting and solidification processes. It results in a growth of micro-cones on the surface. Recently, a problem of a controllable, direct laser fabrication of sharp conical structures on silicon thin films has attracted a significant interest [1, 2, 3]. The laser irradiation causes melting of the material, which is followed by the solidification after the laser pulse. If the solid has a smaller density than the liquid, then the melt is pushed upwards at the end phase of this process, resulting in a characteristic conic shape of the surface. A model is proposed, which allows us to calculate the surface profile by solving a system of two nonlinear differential equations, if the shape of the solid-liquid interface is known. The latter can be found by solving the two-phases Stefan problem. Example calculations have been performed by the fourth-order Runge-Kutta method, assuming that the solid-liquid interface has cylindric symmetry with a parabolic shape of cross section.