The mechanism of radical copolymerization of styrene and maleic anhydride in a homogeneous medium has been studied in the paper. A mathematical model has been built on the basis of the radical copolymerization mechanism of styrene and maleic anhydride. The mathematical model is a system of ordinary differential equations. A numerical solution of the target system enables to determine the average molecular properties such as average number and average weight molecular weights. The calculations based on the model correspond to the experimental data.