The kinetics of the initial growth stages of cadmium telluride (CdTe) films on silicon substrates covered with silicon carbide (SiC) buffer layers grown by the method of topochemical substitution of atoms is investigated theoretically. The model based on the classical nucleation theory is proposed to depict the CdTe film growth by the method of thermal evaporation and condensation in vacuum. The model accounts for the mechanical stresses caused by the lattice mismatch and difference of thermal expansion coefficients of CdTe film and substrate. The influence of substrate and evaporator temperature on the nucleation mechanism and kinetics of the initial growth stages of CdTe film is estimated. The different growth regimes of CdTe films on the SiC/Si substrates are discussed, and the optimal growth conditions are found. It is shown that the elastic stresses in the CdTe/SiC/Si structure are approximately three times lower than the elastic stresses in the CdTe film grown coherently on the Si substrate without the SiC buffer layer. This leads to the large difference in the nucleation rates of the CdTe films on the SiC/Si substrate and Si substrate. The diagram of the nucleation rates of CdTe islands on the SiC/Si depending on the substrate and evaporator temperature is presented.