The directional dark-field signal obtained with X-ray grating interferometry yields direction-dependent information about the X-ray scattering taking place inside the examined sample. It allows examination of its morphology without the requirement of resolving the micrometer size structures directly causing the scattering. The local morphology in turn gives rise to macroscopic mechanical properties of the investigated specimen. In this study, we investigate the relation between the biomechanical elasticity (Young's modulus) and the measured directional dark-field parameters of a well-defined sample made of wood. In our proof-of-principle experiment, we found a correlation between Young's modulus, the average dark-field signal, and the average dark-field anisotropy. Hence, we are able to show that directional dark-field imaging is a new method to predict mechanical sample properties. As grating interferometry provides absorption, phase-contrast, and dark-field data at the same time, this technique appears promising to combine imaging and mechanical testing in a single testing stage. Therefore, we believe that directional dark-field imaging will have a large impact in the materials science world.