We have calculated the structure, electronic and elastic properties of MAlH4(M=Na,K) based on density functional theory. We found both NaAlH4 and KAlH4 are insulators and are characterized by Al—H covalent bond and M—AlH4 ionic bond. The elastic constants are small compared with those of other compounds (e.g MgH2) and decrease in the MAlH4(M=Li,Na,K,Rb,Cs) series. We explain this phenomenon according to the volume change of MAlH4(M=Li,Na,K,Rb,Cs) .