The stability and lattice vibration of H24AlXO20S2 (X = Na, Rb, Cs, K) hydrides are predicted by calculating the crystal structure and energy. The formation enthalpy proves the structural stability and the dynamic stability of the hydride is predicted by the phonon dispersion diagram. Meanwhile, the optical and mechanical properties are analyzed by using the quasi-Debye model. The elastic constants and modulus prove H24AlXO20S2 (X = Na, Rb, Cs, K) mechanical stability. By the value of B/G and Poisson's ratio, it inferred that H24AlNaO20S2, H24AlRbO20S2 and H24AlKO20S2 are brittle. Only H24AlCsO20S2 is ductile and has the lowest hardness. H24AlRbO20S2 has the largest shear modulus and Young's modulus, so it has the highest hardness. In addition, by calculating the anisotropy index of the hydrides, it is proved that they are anisotropic. H24AlKO20S2 has the strongest anisotropy and the value of AU is 0.2477. The anisotropy of the hydride is further studied by calculating the Debye temperature and sound velocity of H24AlXO20S2 (X = Na, Rb, Cs, K) hydrides. The energy band and state density analysis reveal their electronic transitions and bonding.