An accurate knowledge of the elastic properties of materials is essential for material science and engineering applications. Four single crystals of nonstoichiometric alumina-rich spinel [Mg1-xAl2(1+x/3)O4] were obtained from sintered transparent ceramics for the investigation of its elastic properties. The disordered crystal structures were fully resolved by combining single-crystal structure refinement and a quadratic programming approach for the first time. The bond valence model and Brillouin scattering experiments were used to evaluate the bulk modulus (K), shear modulus (G), Young's modulus (E), and Poisson's ratio. The discrepancy between the theoretical and experimental results is <2.6%. The independent elastic constants (C11, C12, and C44) were determined from Brillouin scattering experiments. A negative Poisson's ratio, υ(110, 11̅0), was found to exist in all alumina-rich spinels, which means it is a partially auxetic material. Blackman diagram analysis was introduced to identify the interrelationships and trends in mechanical and bonding properties in alumina-rich spinels. The bond valence model was suggested to be an effective and accurate approach for predicting the elastic modulus of spinels, which provides a useful tool for the study of the composition-structure-property relationship of materials.