Optimising the performance of an internal combustion engine requires both empirical and theoretical work. The latter involves reasoning based on results yielded by mathematical models. This paper presents a computationally efficient model of the working cycle for a compression ignition engine. The model enables analysis of the working cycle of an engine with an electronically controlled common-rail type power supply and a controlled exhaust gas recirculation system. The model’s parameters are chosen in a two-stage identification process based on the results of the experiments. The first stage of identifying the parameters requires formulating and solving an appropriate dynamic optimisation problem for multiple discrete points describing the engine’s operation. To this end a genetic algorithm is used with an additional condition controlling the quality of the solution. Artificial neural networks are used for the second stage of identification. The paper shows an example of using the model to assess the influence of the kinetic combustion phase, which results from the way in which the injection process proceeds on the course of the working cycle. The accuracy of calculations with respect to basic parameters characterising the working cycle is also discussed.