  Rare-earth doped crystals have numerous applications ranging from frequency
metrology to quantum information processing. To fully benefit from their
exceptional coherence properties, the effect of mechanical strain on the energy
levels of the dopants - whether it is a resource or perturbation - needs to be
considered. We demonstrate that by applying uniaxial stress to a rare-earth
doped crystal containing a spectral hole, we can shift the hole by a controlled
amount that is larger than the width of the hole. We deduce the sensitivity of
$\rm Eu^{3+}$ ions in an $\rm Y_2SiO_5$ matrix as a function of crystal site
and the crystalline axis along which the stress is applied.
