The mechanical behavior of soils may be approximated using different models that depend on particular soil characteristics and simplifying assumptions. For this reason, researchers have proposed and expounded upon a large number of constitutive models and approaches that describe various aspects of soil behavior. However, there are few material models capable of predicting the behavior of soils for engineering applications and are at the same time appropriate for implementation into finite element (FE) and multibody system (MBS) algorithms. This paper presents a survey of some of the commonly used continuum-based soil models. The aim is to provide a summary of continuum-based soil models and examine their suitability for integration with the large-displacement FE absolute nodal coordinate formulation (ANCF) and MBS algorithms. Special emphasis is placed on the formulation of soils used in conjunction with vehicle dynamics models. The implementation of these soil models in MBS algorithms used in the analysis of complex vehicle systems is also discussed. Because semiempirical terramechanics soil models are currently the most widely used to study vehicle/soil interaction, a review of classical terramechanics models is presented in order to be able to explain the modes of displacements that are not captured by these simpler models. Other methods such as the particle-based and mesh-free models are also briefly reviewed. A Cam–Clay soil model is used in this paper to explain how such continuum-mechanics based soil models can be implemented in FE/MBS algorithms.