Compaction characteristics of granular materials subjected to axial loading are investigated for both sphere and non-sphere granular assemblies. The computational study is based on the discrete element method (DEM). The compressive stress–strain relation obtained from three-dimensional DEM simulations is compared with that of an idealized two-dimensional plane-strain compression test and physical experiments using a bronze sphere assembly. We observed good agreement between the experimental and three-dimensional DEM simulation results, while two-dimensional simulations significantly underestimate the stiffness of particulate bed, particularly at large strains. This demonstrates that two-dimensional analysis is generally inadequate to model the compaction characteristics of granular systems. We performed a detailed analysis on the force–transmission characteristics of granular materials at microscopic level and present a connection between the directional orientation of force-networks and the invariants of the macroscopic stress tensor: the non-sphere systems were able to build up a strongly anisotropic network of heavily loaded contacts. Several complex phenomena, both geometric and kinematic, that are operative in sphere and non-sphere assemblies due to inter-particle interactions during compression are presented here. It is often assumed that the ratio of invariants of the stress tensor is uniform and constant in uni-axial compression tests. Our results show that the ratio of invariants of the stress tensor is non-uniform and non-constant even when the granular assemblies are subjected to the so-called uni-axial compressive loading, which is in agreement with other recent studies (e.g. Gu et al 2001 Int. J. Plasticity 17 147) performed using the finite element method. The non-homogeneous characteristics that are reported at the particulate scale need to be accounted in considering possible continuum models for the granular systems.