A theoretical study of the process destruction of a solid surface under the action of a powerful radiation impulse is carried out. The peculiarities of the dynamics the surface destruction of the material and the features of the space-time dynamics of the gaseous phase were studied. This phase occurs as a result of local phase changes on the surface of the irradiated material. The differential equation to describe the dynamics of the corrosion crater formation on a solid surface was researched. This equation is analyzed together with equation of near-surface pressure dynamics. The asymptotic analysis for crater equation gives the basis to assert that mathematical interpretation of process of destruction corresponds to actual temporal dynamics of formation of a crater on the substance. The numerical simulation of the formation of a nanocrater with a model form of an active laser impulse is given. The test calculations correspond to experimental observation and theoretical ideas about the process of development of a corrosion crater under laser pulsed irradiation.