A novel tire-soil interaction model that is based on compliant multibody dynamics and soil dynamics theory is presented in this study. This new method models the wheel assembly as a rigid body, and the compliance of the tire and the soil as combinations of springs and dashpots. The two dimensional tire model includes straight lugs, since their presence has a significant impact on traction performance. Tire pressure acting on the soil is calculated and used to determine the soil thrust. The soil stiffness and damping are modeled using a soil dynamics formulation adapted from geotechnical applications. A combination of Coulomb friction at tire-soil interface and earth pressure theory is used to calculate the traction generated by the rolling of the wheel-tire assembly, and determine the occurrence of slip. The methodology presented in this study takes into account the friction between the soil and the tread material and the carcass-soil contact, in addition to the traction provided by the interaction between the lug and the soil. This is different than the traditional Bekker's methodology where the traction generated by the tires is considered to be solely dependent on the static shear strength of the soil. The tire-soil interaction model is implemented in MATLAB. The derivation of the kinematic equations of the wheel-tire assembly is done via MAMBOtoolbox, a Maple-based symbolic manipulation toolbox. The visualization of the results is achieved through the use of MAMBO, a freeware multibody dynamics simulation package. Results of initial 2-D simulations are given for a case study involving an agricultural tire. The methodology is promising in terms of computational efficiency and simulation accuracy. The results illustrate that the model performs reasonably well for traction simulation of off-road vehicles. The key characteristic of the model is the fact that the tire-soil interaction model was developed to be insensitive to the homogeneity of the terrain.