The first-principles calculations of the elastic constants and isotropic moduli of the stoichiometric aluminum oxynitride (Al-O-N) phases, have been examined using the Constant-Anion-Model. The trend in decreasing c(44) of these systems is observed with lower nitrogen content. The shear and bulk properties are in excellent agreement with available experimental data. (C) 2010 Elsevier B. V. All rights reserved.