Low-frequency phonon modes of DNA and RNA molecules can serve as a signature of their structure, flexibility and, hence, their biological function. To investigate the relationship between RNA structure and far IR absorption spectra, we performed FTIR measurements on RNA molecules with known sequence in the spectral range from 10 cm-1 to 25 cm-1 and calculated their internal vibrations. To understand which phonon modes are determined by a double helical topology of nucleic acids, we compared the spectra of single stranded and double stranded RNA molecules. Homopolymers PolyA, polyU, polyC, and polyG, and double stranded homopolymers PolyA-polyU and polyC-polyG were investigated. Theoretical conformational analysis of the double stranded RNA molecules was performed and utilized to calculate the low-frequency vibrational modes. Conformational energy was minimized in the space of internal coordinates of a molecule using standard A-helical topology as an initial approximation. Normal modes were calculated as eigenfrequencies and eigenvectors of the matrix of energy second derivatives. Oscillator strengths were calculated for all the vibrational modes in order to evaluate their weight in the absorption spectrum of a molecule. The obtained phonon modes were convoluted to derive the far IR spectrum of a molecule. These predicted spectra were compared to those obtained by FTIR spectroscopy. Our results confirm that very far IR absorption spectra of biopolymers reflect specific dynamical properties resulting from their structure and topology and, therefore, can be used as fingerprints for specific molecules.