Hydrocarbon feedstock pyrolysis is an important method for obtaining monomers that are then used to produce various polymer materials. During this process, a mixture of hydrocarbons is heated at a high temperature and in the absence of oxygen. Because of the side reactions of polymerization and polycondensation, coke products are formed and settle on the inner walls of the coil. This decreases the technical efficiency of the hydrocarbon pyrolysis furnace during its operation, making the process unsteady. In the present research, we developed an unsteady-state mathematical model of hydrocarbon feedstock pyrolysis in order to improve the monitoring, forecasting, and optimization of this technological process. This model can calculate the rate of coke deposition along the length of the coil, considering the technological parameters and the composition of the supplied raw materials (the calculated value of coke deposition rate equals 0.01 mm/day). It was shown that with an increase in the propane/butane ratio from 4/1 to 1/4 mol/mol, the ethylene concentration decreases from 3.45 mol/L to 3.35 mol/L.