The Brillouin light scattering technique was used to determine experimentally the three independent elastic constants of cubic aluminum oxynitride at the ambient condition. They are C11=334.8GPa,C12=164.4GPa, and C44=178.6+/- 1.1GPa. Its bulk modulus is 221.2 GPa. The magnitude of Zener anisotropic ratio is 2.1 similar to other spinels. The anisotropic nature of the material is shown by a large variation in the Young's modulus and Poisson's ratio with crystallographic directions. The material was found to be auxetic in certain orientations.