Modern Finite Element Analysis (FEA) techniques allow for accurate simulation of various non-linear systems. However they are limited in their simulation of particulate matter. This research uses smooth particle hydrodynamics (SPH) in addition to FEA techniques to model the properties of soils, which allows for particle-level replication of soils. Selected soils are simulated in a virtual environment and validated using the pressure-sinkage and shear tests. A truck tire model is created based on standard heavy vehicle tires and validated using static deflection, contact footprint, and dynamic first mode of vibration tests. The validated tires and soils are used to create a virtual terrain and the tire is placed on the soil, loaded, and run over the soil at various speeds. The results of these simulations show that the SPH modeling technique offers higher accuracy than comparable FEA models for soft soils at a higher computational cost. Further, the SPH models show rolling resistance and tire forces in good correlation with available experimental data. The purpose of performing this research is to develop an off-road rigid ring model in future work.