A new approach to soot formation process that details the acetylene pathway to soot particles has been developed. The model is based on the idea of the fast process of polyynes C2nH2 (n = 2, 3,...) polymerization resulting in primary soot particles in the form of polymeric globules. Soot nuclei arise in the model as radical centers of the polymerization process. Their irreversible growth is conditioned by the occurrence of supersaturation of a polyyne vapor in the chemical reactive atmosphere. The carbonization process of primary soot particles is presented in the model as well. Its duration determines how long soot particles coalesce in the coagulation process. The computer code of the model comprises a detailed description of gas-phase and heterogeneous reactions, soot particle nucleation, surface growth, and coalescence. The principal quantities of the soot formation process, such as the induction time, the soot particle number density, and the soot volume fraction are available in the model. Calculations performed earlier for methane, acetylene, ethylene, and benzene agree well with experiments. The quantitative explanation of the experimental data on pyrolysis of naphthalene/acetylene mixtures is presented in this work. The experimental results on those mixtures are crucial for understanding the soot formation mechanism.