Material strain has recently received growing attention as a complementary resource to control the energy levels of quantum emitters embedded inside a solid-state environment. Some rare-earth ion dopants provide an optical transition which simultaneously has a narrow linewidth and is highly sensitive to strain. In such systems, the technique of spectral hole burning, in which a transparent window is burned within the large inhomogeneous profile, allows one to benefit from the narrow features, which are also sensitive to strain, while working with large ensembles of ions. However, working with ensembles may give rise to inhomogeneous responses among different ions. We investigate experimentally how the shape of a narrow spectral hole is modified due to external mechanical strain, in particular, the hole broadening as a function of the geometry of the crystal sites and the crystalline axis along which the stress is applied. Studying these effects is essential in order to optimize the existing applications of rare-earth-doped crystals in fields which already profit from the more-well-established coherence properties of these dopants, such as frequency metrology and quantum information processing, or even suggest alternative applications of these materials, for example, as robust devices for force-sensing or highly sensitive accelerometers.