The structural parameters, Raman/IR spectra, and vibrational and thermodynamic properties of α-RDX and γ-RDX were investigated by performing first-principles calculations using the CASTEP program. The obtained structural parameters and vibrational frequencies of the internal modes of α-RDX are consistent with previous results. The vibrational bands of γ-RDX in the region 300–3113 cm−1 were assigned to vibrational modes for the first time. Furthermore, the thermodynamic properties of α-RDX and γ-RDX were calculated, including the constant-volume specific heat Cv, entropy S, Helmholtz free energy F, enthalpy H, and Gibbs free energy G.