Modeling of soil compaction processes in agriculture provides a means to evaluate harmful vs. desired soil compaction. The steps involved in the development of a basic soil compaction simulation model include: (1) prediction of surface applied forces from farm vehicles; (2) representation of soil stress-strain relationships; (3) modeling the propagation of stresses in the soil profile. Simple relationships are available that predict the surface stress from easily measurable parameters, such as inflation pressure, applied load and tire characteristics. Because of the presence of lugs on tires, prediction of surface stress is much more complicated and needs additional research. Stress-strain relationships obtained from both uniaxial or triaxial laboratory tests have been shown to be adequate for describing soil compaction from farm vehicles. In general, uniaxial tests are easy and inexpensive, whereas triaxial tests are more accurate and apply to many different soil conditions. All existing models of stress propagation in soil are based on the theory of elastic deformation. These models can be categorized into two groups: finite element models and analytical models. Both groups of models have been shown to be adequate for a limited set of experimental conditions. Much more research is needed to make these models acceptable in everyday use by researchers and practitioners. The procedures to link soil compaction models to crop growth models and the research needed both in methods to estimate parameters of the model and in describing the missing processes are also discussed.