There are large differences between theoretical and experimental reports on the phase transition points of alkali alanates, which motivated us to study the pressure phase transitions using Density Functional Theory. After applying the pressure, the band gaps were narrowed from 5 eV to the extent of 1.94 eV. The density of states plots clearly shows the non-metallic characteristic of all structures under pressure. Moreover, we compared the results using the PBE and PBEsol exchange-correlation functionals, with available experimental data. The agreement between experimental and the PBEsol values was superior over the PBE functional. RbAlH4 complex undergoes a structural transformation from orthorhombic (Pnma) to tetragonal (I4(1)/a) structure, under the pressure of 3.2 GPa. There was a subsequent transition to the Cmc2(1) at 6.8 GPa, which is reported here for the first time. In the CsAlH4 case, the tetragonal (I4(1)/a) structure was more stable, but a small energy difference with orthorhombic (Pnma) structure was observed. Under the high pressure, both phases changed to the other, which is in parallel with the experimental reports. (C) 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.