This paper conducts a three-dimensional (3D) modeling study to investigate the hydrogen absorption process and associated mass and heat transport in a metal hydride (LaNi5) hydrogen storage tank. The 3D model is further implemented numerically for validation purpose and the detailed investigation on absorption process. Results indicate that at the very initial absorption stage the bed temperature evolves almost uniformly, while it varies greatly spatially at the latter stage. At the initial seconds, most hydrogen is absorbed in the region near the cooling wall due to the better heat removal. The absorption in the core is slow at the beginning, but becomes important at the very end stage. It also shows that the initial hydrogen flow in the bed is several-fold larger than the latter stage and the flow may provide extra cooling to the hydriding process. By analyzing the Peclet number, we find that the heat convection by the hydrogen flow may play an important role in local heat transfer. This work provides an important platform beneficial to the fundamental understanding of multi-physics coupling phenomena during hydrogen absorption and the development of on-board hydrogen storage technology.