The Shell autoignition model with the value of the pre-exponential factor in the rate of production of the intermediate agent (A(f4)) in the range between 3 x 10(6) and 6 x 10(6) has been applied to the detailed modelling of the ignition process in monodisperse and polydisperse sprays based on a computational fluid dynamics (CFD) code. The mass balance in the Shell model has been improved to ensure better physical consistency and more effective numerical implementation. Based on the analysis of the ignition in a monodisperse spray it is pointed out that in the case of droplets with the initial radius (R-d0) about or greater than 6 mum the physical ignition delay dominates over the chemical ignition delay, while for the smaller droplets with R-d0 less than or equal to 2.5 mum the opposite is true. The start of the ignition process is predicted near the periphery of both monodisperse and polydisperse sprays in agreement with current understanding of this phenomenon. The observed ignition delay for a monodisperse spray agrees with the available experimental data. The ignition stage of the polydisperse Diesel combustion predicted by the model agrees with available experimental data for a medium duty truck Diesel engine, provided that the fine tuning of the parameter A(f4) is performed and additional constants, such as concentration limits. are introduced.