This paper presents a numerical study on the packing density and bed orderness in packing and vibration of ellipsoids by discrete element method (DEM). The shapes considered are oblate and prolate spheroids, with aspect ratio varying from 0.15 to 4.0. It is shown that under the poured packing conditions of coarse ellipsoids, flat or elongate particles show strong orientation preference on the horizontal direction. For packing with different particle sizes, when increasing particle size, packing density increases, global orientational order increases. For the cases of packing under one-dimensional vibration with periodic boundary condition and cylindrical wall conditions, after vibration, packing density increases, but global orientational order decreases. Boundary condition affects packing structure under both poured packing and vibration conditions. Under the cylindrical wall condition, considerable part of oblate particles have the symmetry axis pointing to the horizontal direction and quite a number of prolate particles have the symmetry axis pointing to the vertical direction after vibration. For spheres, denser packing leads to more (positional) ordered structure. For ellipsoids, denser packing can either be more (global and local orientational) ordered or random packing, which implies it does not necessarily be ordered packed to obtain higher packing density. (C) 2019 Elsevier B.V. All rights reserved.