For a case of chemical reactions of the first order the mathematical model of process of chemical cutting of crystals is advanced. It is showed, that the return speed of chemical cutting is equal to the sum of return speeds of such values, as velocity of a chemical reaction, velocity of delivery etchant and speed of diffusion of molecules of a reactant. At research of process of chemical cutting of crystals InSb the satisfactory coordination between experimental and theoretical results is obtained. The developed model can be used at designing of the equipment and for optimization of process of chemical cut.