The crystal α-AlH3 , the most stable polymorph of alane under ordinary conditions, is a perspective material as a hydrogen source for portable fuel cells due to its large volumetric and gravimetric hydrogen density [1]. Earlier it was shown [2], that the hydrogen desorption from α-AlH3, caused by the presence of hydrogen vacancies , becomes significantly faster after UV irradiation. However, a mechanism of UV activation of dehydriding process is not yet clear. To clarify it the information about the processes of light absorption in the UV range is necessary. First of all it is of interest whether the absorption of ultraviolet light is due to the perfect crystal or some defect center. In order to find this out we carried out the band structure and absorption spectrum calculations of the perfect α-AlH3 crystal. We used the DFT method implemented within CASTEP code package [3], which employs a plane wave basis set for valence electrons, the atomic core being incorporated by norm-conserving p