The vibrational spectra of the alpha, beta, and delta phases of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) have been investigated by complimentary theoretical and experimental approaches. Density functional theory and the scaled quantum mechanical force-field method have been used to calculate the vibrational spectra of the H8C4N8O8 molecule in C-i and C-2v symmetry conformations in the gas phase. By comparing the calculated molecular vibrational frequencies of the H8C4N8O8 molecule with the experimental infrared and Raman spectra of HMX crystalline samples, we attempt to assign the intramolecular motions that correspond to the measured bands in the experimental spectra of HMX in alpha-, beta-, and delta-phase crystal lattices. Our analysis of the vibrational spectra verifies that the particular conformation of the H8C4N8O8 molecule in each crystal lattice of HMX determines, to a great extent, the general pattern of the vibrational spectrum of the crystal lattice. We also compare our detailed motion assignments with the general assignments proposed in previous experimental work. Good agreement is found between the calculated geometry of the H8C4N8O8 molecule in the Ci symmetry conformation and the experimental geometry of molecules in the beta-phase lattice of HMX and between the calculated geometry of the H8C4N8O8 molecule in the C-2v symmetry conformation and the experimental geometry of molecules in the alpha- and delta-phase lattices of HMX.