Focusing on characterizing the elastic behavior of the granular particles based on the discrete element method (DEM), this study utilized the Mustoe and Griffiths’ equations and a homogenization method to predict the performance of the continuous elastic medium precisely, including the elastic modulus, Poisson’s ratio, and the brittle fracture criterion. A commercial DEM software named Particle Flow Code in Two Dimensions (PFC2D) was used to conduct the numerical simulations because the macrobehavior predicted by the PFC2D highly depends on the sphere size and arrangements. The hexagonal parking arrangements were applied further herein for better theoretical calculations. With the combined analysis of the discontinuum theory and continuum theory, the DEM parameters were determined theoretically and were verified based on the virtual compression and tension tests. The factors (including sphere size, stiffness ratios, etc.) influencing the prediction accuracy were also analyzed further. The results showed that by the parameter determination methods proposed in this study, the behavior of the continuous elastic medium could be well characterized.