Pressure effects on the vibrational structure of alpha-RDX were examined using density functional theory (DFT) up to 4 GPa. The calculated vibrational frequencies at ambient conditions are in better agreement with experimental data than are previous single molecule calculations. The calculations showed the following pressure-induced changes: (i) larger shifts for lattice modes and for internal modes associated with the CH2 and NO2 groups as compared to the pressure shifts for modes associated with the triazine ring, (ii) enhancement of mixing between different vibrations, for example, between NN stretching and CH2 scissor, wagging, twisting vibrations, and (iii) increase in mixing between translational lattice vibrations and the NO2 wagging vibrations, reducing the distinction between internal and lattice modes. The calculated volume and lattice constants at ambient pressure are larger than the experimental values, due to the inability of the present density functional approach to correctly account for van der Waals forces. Consequently, the pressure-induced frequency shifts of many modes deviate substantially from experimental data for pressures below 1 GPa. With increasing pressure, both the lattice constants and the frequency shifts agree more closely with experimental values.