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This report addresses the development of experimental and computational estimations of the anisotropic elastic moduli (EM) of single crystals to aid in the a priori (i.e., starting with the crystal structure) prediction of the trend as a function of the direction of applied stress. Experimentally EM values in the normal direction to the X-, Y- and Z-planes of block shaped aspirin and acetaminophen crystals were determined using data generated by the newly designed compression stage housed in our powder X-ray diffractometer. Computational estimations of EM were made using the applicable modules in Material Studio® 5.5. The measured EM values normal to the (1 0 0), (0 2 0) and (0 0 2) planes of aspirin, and (2 0 −1), (0 2 0) and (0 0 1) planes of acetaminophen crystals by both methods succeeded in detected the anisotropic behavior. However, disparity in the relative values between measured EM values by different techniques was observed. This may be attributed to deformation sources other than lattice compression including inelastic processes such as local failure and plasticity as well as deformation at the crystal–probe interfaces due to crystal surface roughness (asperities). The trend of the ratio of the values from the respective methods showed reasonable agreement and promise for the technique. The present approach demonstrated the suitability of the compression stage to determine and predict anisotropic EM of subjected small molecular organic crystals.