Recent developments in high-pressure X-ray studies enable the measurement of the elastic strain anisotropy induced by a macroscopic differential stress in an aggregate sample. Such data are commonly used to constrain the single-crystal elastic moduli under the assumptions of the Reuss-Voigt state. We find this procedure is valid only for samples that have not been plastically deformed. Measured elastic strain anisotropy for MgO at stress levels below the yield point agree well with the Reuss elastic model. Plastic deformation effects a change in the stress field for subpopulations of grains that represent different crystallographic orientations with respect to the applied stress field. Our data for the plastically deformed sample are consistent with the predictions of a self-consistent aggregate model for deforming polycrystals. Such models may be useful as a guide to define the elastic properties in light of the active slip systems.