The discovery of auxetic behavior (negative Poisson's ratio) within elements and alloys had focused attention on their elastic anisotropy in an effort to understand the range of crystal orientations that manifest this property. A comparison of elastic constant data to atomistic models based on pair-wise, central force models provides key insights into deformation behavior of cubic crystals over a wide range of anisotropy, including, for the first time, those with Zener anisotropy ratios less than 1. A simple criterion is derived which dictates all cases in which a crystal whose atomic ordering obeys cubic symmetry will display auxetic deformation, where the extrema in Poisson's ratio involves (110) orientations. In the field of stress determination through x-ray diffraction, these findings also shed light on strain anisotropy in polycrystalline materials, where the elastic incompatibility between adjacent grains alters their overall deformation. By applying these same atomistic models, we can predict the Voigt/Reuss weighting fractions associated with Kröner limit x-ray elastic constants for cubic materials, a necessary component in quantifying stress using diffraction data. We also establish that greater elastic anisotropy in a constituent crystal leads to a more rigid mechanical response in the corresponding polycrystalline aggregate, with implications for auxetic crystal ensembles.