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Based on the density functional theory within plane-wave pesudopotential method, the band structure and elastic properties of spinel Al(64+x)/3 square(8-x)/3O(32-x)Nx (x = 2, 5, 8) and alpha-Al2O3, AlN are calculated. The spinel Al(64+x)/3 square(8-x)/3O(32-x)Nx (x = 2, 5, 8) are calculated by using the 'virtual crystal approximation'. The results prove it possible to study the Al(64+x)/3 square(8-x)/3O(32-x)Nx (x = 2, 5, 8) by this approximation. The calculated elastic constants and hardness features accord well with the experimental results. The five structures in the Al2O3-AlN solid solution region all show brittle features and the Al23O27N5 shows the lowest brittleness. High hardness and low brittleness reflect that Al23O27N5 has a great flexural strength. Elastic property analysis confirms the mechanical stability, it also reveals that AlON has highly elastic anisotropy. Band structure analysis shows that the spinel AlON and alpha-Al2O3, AlN are both direct bandgap materials. Hybridizations take place between Al-3p, 3s and 0, N-2p orbitals near the Fermi level in the AlON. The calculated results are consistent with relevant experimental results, which provides a theoretical method and reference for the further study.