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Discrete element method (DEM) has been widely used to study granular materials. However, how to model non-spherical particles is still challenging. Ellipsoidal particles are a typical kind of non-spherical particles in DEM simulations. There are three common methods to calculate the overlap and contact force between two ellipsoidal particles, namely, geometric potential (GP), common normal (CN) and overlap region (OR) methods. These methods are based on different physical concepts and hence will give different results. However, the comprehensive evaluation of these methods is still lacking, leaving DEM users no solid reference for selecting algorithms. In this paper, we conduct detailed comparisons on the penetration depth, contact plane and contact point predicted by the three methods. Particularly, using the orientation discretization method, the results are compared in all orientations quantitatively. It is …