To gain insight into the high-pressure polymorphism of RDX, an energetic crystal, Raman spectroscopy results were obtained for hydrostatic (up to 15 GPa) and non-hydrostatic (up to 22 GPa) compressions. Several distinct changes in the spectra were found at 4.0 +/- 0.3 GPa, confirming the alpha-gamma phase transition previously observed in polycrystalline samples. Detailed analyses of pressure-induced changes in the internal and external (lattice) modes revealed several features above 4 GPa: (i) splitting of both the A' and A '' internal modes, (ii) a significant increase in the pressure dependence of the Raman shift for NO2 modes, and (iii) no apparent change in the number of external modes. It is proposed that the alpha-gamma phase transition leads to a rearrangement between the RDX molecules, which in turn significantly changes the intermolecular interaction experienced by the N-O bonds. Symmetry correlation analyses indicate that the gamma-polymorph may assume one of the three orthorhombic structures: D-2h, C-2v, or D-2. On the basis of the available X-ray data, the D-2h factor group is favored over the other structures, and it is proposed that gamma-phase RDX has a space group isomorphous with a point group D-2h with eight molecules occupying the C-1 symmetry sites, similar to the alpha-phase. It is believed that the factor group splitting can account for the observed increase in the number of modes in the gamma-phase. Spatial mapping of Raman modes in a non-hydrostatically compressed crystal up to 22 GPa revealed a large difference in mode position indicating a pressure gradient across the crystal. No apparent irreversible changes in the Raman spectra were observed under non-hydrostatic compression.