The properties of the complex hydrides LiBH4 and NaAlH4 such as structural, electronic, and optical properties were calculated using the augmented plane wave plus local orbitals (APW + lo) method. The three phases alpha, beta, and gamma of LiBH4 and NaAlH4 hydrides are studied, the beta-phase is transformed at the high-pressure to gamma phase for the compound LiBH4 with the generalized gradient approximation (GGA) with a 16% volume decrease. However, NaAlH4 compound did not show any phase transition. The interaction between the boron (aluminum) atoms and the hydrogen atoms in the [AlH4](-) ([BH4](-)) complexes is strongly covalent, and between the complexes [AlH4](-) and the lithium Li+ cations for the LiBH4 compound and between the complexes [AlH4](-) and the sodium Na+ cations for the NaAlH4 compound, the bond is ionic. For the most stable phases of the two complex hydrides, different optical parameters have been calculated as a function of the photon energy. The plasma frequency omega(p) is calculated from the mean peak of the energy loss function. Therefore, by way of example, the plasma energy h omega(p) of its peak position is 13.23 (12.93) eV for alpha-NaAlH4 (alpha-LiBH4).