We report here the experimental and computational results of a high‐pressure study (up to 40 GPa) of yttrium borohydride. During compression in neon pressure medium the cage‐like RuO3 structure of α‐Y(BH4)3 is stabilized by the formation of the inclusion compound with this chemically inert gas. Ne atoms fill the voids available in the crystal structure of the host at the special 0 0 0 and 0.5 0.5 0.5 positions. The inclusion compound preserves high crystallinity up to ca. 10 GPa, while gradual amorphization is observed at higher pressures. The results of our DFT calculations indicate that although the molecular volumes of the tested system are rather well modeled using PBEsol functional, significant improvement, especially in terms of the phases' relative energy can be made when applying dispersion correction, using PBE‐TS approach.