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NO and soot emissions from Diesel engines are dependent on several parameters related to the engine design and operating conditions. Multidimensional models are increasingly employed to study the effect of these parameters. In this paper, a multidimensional model for flows, sprays and combustion in engines is employed to study the dependence of NO and soot formation and oxidation on injection timing, injection pressure, chamber temperature, EGR and ignition delay, and compare the computed trends with those observed in experimental studies reported in the literature. Computations are carried out in a typical heavy-duty Diesel engine and additional computations in a constant volume chamber are used to clarify the engine results when appropriate. For several parametric changes, the experimentally observed trends are reproduced. However, several limitations are identified. The structure of the computed combusting jet has differences with those suggested from recent experiments.