We present Raman studies of the vibrational properties of 3,4,9,10-perylene tetracarboxylic dianhydride (PTCDA) single crystals. Davydov splitting of internal molecular vibrations due to the interaction of two molecules in a unit cell was observed. Features of PTCDA crystal lattice vibrations in the low-frequency region of the Raman spectra are reported. PTCDA films deposited on passivated Si and GaAs surfaces also reveal the specific features of crystalline structure: Davydov splitting and appearance of phonon lines in Raman spectra.