Researchers at Caterpillar have been using Finite Element Analysis or Method (FEA or FEM), Mesh Free Models (MFM) and Discrete Element Models (DEM) extensively to model different earthmoving operations. Multi-body dynamics models using both flexible and rigid body have been used to model the machine dynamics. The proper soil and machine models along with the operator model can be coupled to numerically model an earthmoving operation. The soil – machine interaction phenomenon has been a challenging matter for many researchers. Different approaches, such as FEA, MFM and DEM are available nowadays to model the dynamic soil behavior; each of these approaches has its own limitations and applications. To apply FEA, MFM or DEM for analyzing earthmoving operations the model must reproduce the mechanical behavior of the granular material. In practice this macro level mechanical behavior is not achieved by modeling the exact physics of the microfabric structure but rather by approximating the macrophysics; that is using continuum mechanics or/and micromechanics, which uses length scales, that are larger than the physical grain size. Different numerical approaches developed by Caterpillar Inc. researchers will be presented and discussed.