© 2022 Elsevier B.V.Analyses based on first-principles simulations have revealed new details about the mechanical and thermodynamic characteristics of NaBH4 and NaAlH4 complex hydrides in α, β and γ phases. Using the quasi-harmonic Debye model, thermal parameters like the Debye temperature, the heat capacity, and the thermal expansion coefficient of NaXH4 (X = B, Al) complex hydrides are calculated in α, β and γ phases at different pressures and temperatures for the first time. Single-crystal elastic constants may be derived from the stress-strain relationship calculations. Although NaBH4 has a stronger compressibility modulus than NaAlH4, the distance dB-H is shorter than dAl-H, which may be explained by the presence of the covalent bond in BH4 and AlH4 in NaXH4 (X = B, Al). The melting points of NaXH4 (X = B, Al) may be used to estimate the decomposition temperatures of hydrogen. β-NaBH4 has a higher melting point than α-NaAlH4. Thus, the decomposition temperature of NaAlH4 at which hydrogen is released from a fuel cell is expected to be lower than that of NaBH4. β-NaBH4 has a more directed bonding tendency than α-NaAlH4 does. Except for the phase γ-NaAlH4, the NaXH4 (X = B, Al) compounds are ductile. NaBH4 deforms more than NaAlH4 in uniaxial deformation, yet both are centrally strong solids. Our PBE calculations result in the linear compressibility and orientation-dependent Young's modulus. Tetragonal β-NaBH4 and α-NaAlH4 structures have an isotropic bulk modulus but an anisotropic Young's modulus.