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The vibrational spectra of crystalline nitric acid hydrates have been investigated at the periodic ab initio quantum level by using a Gaussian type basis set and the hybrid B3LYP Hamiltonian with CRYSTAL06 code. Using as input the X-ray structures of crystalline nitric acid monohydrate NAM, dihydrate α-NAD and trihydrate β-NAT, the inner coordinates within each unit cell have been optimized. The calculated structures of these atmospherically relevant systems are used in the evaluation of their vibrational normal modes. The obtained theoretical results show in general a good agreement compared to the observed spectra in the range 4000- 600 cm-1 and 200-20 cm-1 for infrared and Low-Frequency Raman spectra, respectively.