The electronic structure, lattice dynamics, and mechanical properties of AlH3 phases have been studied by density functional calculations. The chemical bonding in different polymorphs of AlH3 are evaluated on the basis of electronic structures, charge density analysis, and atomic charges, as well as bond overlap population analysis and the Born effective charges. The phonon dispersion relations and phonon density of states of all the polymorphs of AlH3 are calculated by direct force-constant method. Application of pressure induces seqauence of phase transitions in beta-AlH3 which are understood from the phonon dispersive curves of the involved phases. The previously predicted phases (Chem. Mater. 2008, 20, 5997) are found to be dynamically stable. The calculated single crystal elastic constants reveal that all the studied AlH3 polymorphs are easily compressible. The chemical bonding of these polymorphs have noticeable covalent character (except the hp2 phase) according to the present chemical bonding analyses. For all these polymorphs, the NMR-related parameters, such as isotropic chemical shielding, quadrupolar coupling constant, and quadrupolar asymmetry, are also calculated. All IR- and Raman-active phonon frequencies, as well as the corresponding intensities, are calculated for all the AlH3 polymorphs and are compared with available experimental results.