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The absence of a general theory that describes the dynamical behaviour of the particulate materials makes the numerical simulations the most current powerful tool that can handle many mechanical problems relevant to the granular materials. It provides a potential window and useful insight to answer massive questions related to the multi-state dynamical granular systems, including the prediction of internal particles behaviour within the particulate systems. In this book, based on a two-dimensional soft particle discrete element method (DEM), we study three different granular dynamical problems, namely, the pulsation stress nature and the stress distribution on hopper wall during filling of granular solids into silos and discharging of granular solids from silos, the vertical penetration of projectiles into granular beds, and the normal force distribution underneath granular piles.