Quantum storage of photons in an atomic ensemble can be obtained by using three-level Λ systems. In these schemes, two levels are coupled by optical transitions to a third one. Ideally, the two transitions should have similar intensities and long coherence lifetimes. Rare earth ion doped crystals are attractive materials for quantum storage because their hyperfine levels can have coherence lifetimes longer than 100 μs and thus can be used to build Λ systems. Tm 3+ ions are especially interesting since they can be excited by ultra-stable laser diodes. In this paper, the hyperfine structures of the 3H 6(0) and 3H 4(0) crystal field levels of Tm 3+ in Y 3Al 5O 12 are investigated by hole burning spectroscopy under a magnetic field. The results are compared to theoretical calculations and found to be in reasonable agreement. Moreover, it is shown that an appropriate magnetic field is able to relax the selection rule on the nuclear spin projection, an absolutely necessary condition to obtain an efficient three-level Λ system with Tm 3+ in this host. Finally, a magnetic field orientation optimized with respect to the Λ system transition intensity ratio is predicted for a convenient experimental set-up.