Recent advances in the capabilities of personal, workstation, and cloud computing platforms have spurred developments in many computational fields. Terramechanics, involving the study of the dynamic interactions between vehicle and terrain, could, to great benefit, leverage existing compute power towards the use of higher fidelity models. In this paper, we outline the formulation and implementation of an inelastic continuum based soil model in a multibody system (MBS) simulation environment. Such a new computational environment will allow for the simulation of the complex and dynamic interactions occurring at the interface between tracks and wheels, and the ground. The soil model is developed using the absolute nodal coordinate formulation (ANCF) finite elements. In deformable terrain, soil is modeled as a set of 8-node brick ANCF elements whose mechanical behavior may be defined by a suitable constitutive model. A Drucker-Prager plasticity material, which is used to model the behavior of the soil, is proper for the simulation of a number of types of soils and offers a good starting point for computational plasticity in terramechanics applications. Such higher fidelity terramechanics simulations can be fruitfully applied towards the investigation of complex dynamic phenomena in terramechanics. The proposed ANCF/Drucker-Prager soil model is implemented in a MBS computer code. This implementation is demonstrated using an Armored Personnel Carrier (APC) model.