The objective of this work was to develop simplified soot models for use with a direct injection diesel engine combustion simulation. The soot models, when used with the combustion simulation, were required to be able to predict engine exhaust emissions trends, to be sensitive to major combustion system variables, and yet to be efficient enough to be used with an engine cycle simulation and formal mathematical optimization procedures. The background of soot formation in diesel engines is reviewed and the assumptions for the models are discussed. The resulting models have global soot formation and consumption steps with an Arrhenius temperature dependence. The choice of the model constants, the selection procedure for the constants, and the sensitivity of the constants to engine operating conditions are presented. General considerations for the testing of emissions models and possible extensions of the soot models are discussed. Comparisons of model predictions with the experimental data at several operating conditions demonstrate that the models are sensitive to major combustion system variables, predict the correct soot emissions trends, and are computationally efficient.