The vibrational properties of crystalline Na+ beta-alumina (Na1.22Al11O17.11) have been studied using the molecular dynamics simulation technique. The vibrational density of states was calculated from the velocity autocorrelation function, and the infrared spectrum from the dipole-dipole autocorrelation function. Knowledge of the vibrations in different crystallographic directions for the different atomic species facilitates the assignment of spectral peaks. The sodium in-plane vibrations are 59, 88 and 112 cm-1, and the out-of-plane vibrations are at 146 cm-1. The stoichiometric compound is also studied, and in this case the sodium in-plane vibrations are at 80 cm-1 and the out-of-plane vibrations at 140 cm-1. The density of states is used to calculate thermodynamic properties: heat capacity, entropy and internal and free energy. The values obtained at 300 K are C(upsilon) = 410 J K-1 mol-1, S(upsilon) = 300 J K-1 mol-1, U = 370 kJ mol-1 and F = 280 kJ mol 1. The heat capacity and entropy values are in good agreement with experiment, and thus strongly support the empirical force field used in the simulation