The phenomenon of solid-phase diffusion over the surface of substances accompanied by a chemical reaction is considered. The purpose of the research is to describe the concentration of substances and the surface layer growth of the reaction product. The model, which takes into account the redistribution of diffusion fluxes and the diffusant sublimation, is constructed. It is the system of parabolic equations complicated by a moving unknown boundary. An algorithm for computing the finite-difference solution based on the method of front straightening is developed. Estimation of the characteristic times of the processes observed makes it possible to construct an analytical approximation. Numerical and analytical solutions agree well in a wide range of model parameter values, including limiting cases. This allowed us to identify the law for the surface layer growth with time, which has the order.