The mechanical and thermodynamical features of LiBH4 and LiAlH4 complex hydrides in the α, β and γ phases are evaluated using density functional theory. To our knowledge, thermal parameters such as, the Grüneisen parameter γ, the heat capacity, and thermal expansion coefficient of LiXH4 (X = B, Al) complex hydrides in α, β and γ phases are computed for the first time. The parameters are determined in terms of pressure (0–6 GPa) and temperature (0–600) K using the quasi-harmonic Debye model. The computed stress–strain relationships effectively yield the elastic constants of a single crystal. The estimated elastic constants of α-LiBH4 compound are noticeably higher than those of several closely similar ABH4 (A = Na, K, Rb, and Cs) borohydrides. In the β-LiAlH4 tetragonal structure, the 001 direction is readily compressible as compared to the 100 direction. The compressibility modulus of the LiBH4 compound is greater than that of the LiAlH4. However, the distance between B and H is less than the distance between Al and H. This might be explained by the presence of covalent bonds in BH4 and AlH4 in LiXH4 (X = B, Al). The melting temperatures of LiXH4 (X = B, Al) are used to predict the temperatures of hydrogen decomposition. The obtained melting temperature of α-LiBH4 is higher than that of β-LiAlH4. Thus, LiAlH4's decomposition temperature at which hydrogen is emitted from a fuel cell is anticipated to be lower than that of the LiBH4 compound. The bonding behavior of α-LiBH4 is more directed than that of β-LiAlH4. All the LiXH4 (X = B, Al) are found to be ductile except α-LiAlH4 which is found to be fragile. LiBH4 experiences greater volume change during uniaxial deformation than LiAlH4 and both are centrally strong solids. Our PBE calculations yield the linear compressibility and Young's modulus orientation dependent. The orthorhombic LiBH4 and tetragonal LiAlH4 are isotropic in bulk and anisotropic in Young's modulus. •The computed stress–strain relationships effectively yield the elastic constants of a single crystal.•The compressibility modulus of the LiBH4 compound is greater than that of the LiAlH4.•The orthorhombic LiBH4 and tetragonal LiAlH4 are isotropic in bulk and anisotropic in Young's modulus.•These materials could be useful for storage of hydrogen application.