The transition from random loose packing (RLP) to random close packing (RCP) of mono-sized regular tetrahedral particles under 3D mechanical vibration was modeled by using discrete element method. The effects of vibration conditions and container size on the packing densification were systematically studied, and the macro and micro properties such as packing density, coordination number (CN), particle contact type, radial distribution function (RDF), particle orientation correlation, and forces between particles were characterized and analyzed. The randomness of the obtained dense packings and corresponding densification mechanisms were also investigated. The results show that RCP of the tetrahedral particles can be realized by properly controlling the vibration conditions. And the obtained maximum random packing density can reach about 0.7402 by extrapolating the packing densities in different sized containers. The average CN for RLP and RCP are 7 and 63, and the CN distribution for RCP is higher and narrower than that for RLP. From RLP to RCP, the frequency of face to face (F-F) contact between two particles increases, while that of vertex to face (V-F) contact and edge to face (E-F) contact decreases, and edge to edge (E-E) contact does not change much. RDF characterization shows four obvious peaks on the curves of RLP and RCP, where the height of the first peak (F-F contact) increases while that of other peaks decreases from RLP to RCP. The densification mechanism can be ascribed to the formation of wagon wheel local dense structures through rearrangement by 'pushing filling' and 'jumping filling'. (C) 2017 Elsevier B.V. All rights reserved.