In the context of the design and study of new materials for hydrogen storage, in this work structural, compositional, thermodynamic and kinetic-mechanistic factors for the desorption/absorption of a hydrogen molecule in the M3AlH10-xNa (M = Be or Mg; x = 0 or 2) hydrides are evaluated. The results show that the mechanisms of hydrogen detachment/attachment are energetically more favorable when the two involved hydrogen atoms are related to different metals in each system. The hydrogenation of M3AlH8Na occurs very easily at relatively low temperatures. The most convenient values of temperature and rate constants for thermal dehydrogenation are reached for the Be3AlH10Na system in tetrahedral geometry. These factors, together with the fact that this structure is quite symmetrical, make the tetrahedral Be3AlH10Na a good candidate as an assembly unit for suprastructures. However, our results indicate that the dehydrogenation temperature is rather high; so, future studies about ways to facilitate Be3AlH10Na dehydrogenation, such as its catalysis or its support on some surface, are necessary for energy-based uses.