Adjusting engines with a high compression ratio operating on traditional gasoline grades is simplified by the application of mathematical models of the operating cycle that predict the self-ignition of the fuel-air mixture. Mathematical simulation of detonation based on the analysis of a computational model of the thermodynamic cycle of a spark-ignited piston engine, which is close to the actual cycle, can be used to determine with sufficient accuracy in time the change in the current cycle pressure and the temperature of the unburned part of the charge. The model takes into account the heat exchange between the combustion zones of the charge and the walls of the combustion chamber. The onset of detonation is associated with the point of self-ignition of the unburned part of the charge and is determined depending on the thermodynamic parameters of the unburned part of the charge and the kinetic mechanism of pre-ignition chemical processes in the fuel-air mixture. It is shown that mathematical modeling of the self-ignition of the unburned part of the charge in a spark-ignition piston-type internal combustion engine can be performed in the same way as the modeling of self-ignition of the fuel-air mixture under continuing compression in units with a free-sliding piston. The accuracy of the self-ignition calculation using the cycle model has been experimentally verified by indicating it at different speeds and at different excess air and charge volume ratios, as well as different mixture temperatures in the intake manifold. The simulation results were verified experimentally on isooctane and octane blends (60% isooctane) and on commercial gasoline. It was found that at low compression ratios (up to 5 to 7), the low-temperature mechanism of self-ignition prevails, while at higher compression ratios, the high-temperature mechanism prevails. The detonation limit of an internal combustion engine can be determined by the point of self-ignition (explosion) in the unburned part of the charge at a residual cycle fraction of unburned fuel of at least 10%.