The talk presents Cauchy stress tensor computation over parallel grids of Message Passing Interface (MPI) parallel Three-Dimensional (3D) Discrete Element Method (DEM) simulations of granular materials, considering spherical and non-spherical particles. The stress tensor computation is studied for quasi-static and dynamic conditions, and its resulting symmetry or asymmetry is discussed within the context of classical continuum mechanics (CCM), granular materials mechanics (GMM), and micropolar continuum mechanics (MCM). The average Cauchy stress tensor computation follows Bagi’s and Nicot’s formulations and is verified within MPI parallel 3D DEM simulations involving dynamically-adaptive compute grids. These grids allow calculation of temporal and spatial distributions of stress across granular materials under static and dynamic conditions. The vertical stress component in gravitationally-deposited particle assemblies exhibits non-uniform spatial distributions under static equilibrium, and its zone of maximum value changes during the process of gravitational pluviation and collapse. These phenomena reveal a microstructural effect on stress distribution within granular materials that is attributed to their discrete particulate nature (particle size, shape, gradation, boundary conditions, etc).