We generate the maximally random jammed (MRJ) packings and maximally dense random packings (MDRPs) of bi-axially elongated superballs with different shape parameters. On the MRJ packing state, the packings of ellipsoids, general superellipsoids and cuboids are on different random degrees and the shape elongation effects on the disordered-packing densities are not uniform. The effects of order degree and particle shape are compounded. However, we find uniform shape elongation effects on the MDRP state. Bi-axial elongation will improve the random-packing densities. The packing densities reach the maximum when the aspect ratio is about 1.5 for all the surface shape parameters and oblateness. The influence of order degree is eliminated on the MDRP state, which demonstrates the advantages of the MDRP state as a platform for comparing the packing density of disordered packings. Our work helps to explore the shape effects on disordered packings of non-spherical particles. (C) 2020 Elsevier B.V. All rights reserved.