The external vibrational modes of rhombohedral NaN3 have been studied by means of normal mode calculations and inelastic neutron scattering measurements on powder samples. Phonon dispersion curves and displacement weighted frequency distributions have been computed using force-constant models in which the coupling parameters are determined by fitting the long-wavelength optical frequencies and through the use of interatomic pair potentials. The azide ion is treated in two ways, with and without internal distortions. In both cases short-range interactions involving nearest and next-nearest neighbors are considered in carrying out the lattice calculations. Electrostatic interactions are treated using the standard method of Kellermann and the effective ionic charge is taken to be a parameter. The present method of specifying the model force field enables us to undertake a parameter-free comparison between the calculated and observed spectra of neutrons inelastically scattered from polycrystalline samples of NaN3. Theoretical cross sections have been obtained in the incoherent approximation, but the good agreement between calculations and measurements over an appreciable range of momentum transfers suggests that specifically coherent effects are probably small in the present experiment. Since the neutron data provide a reasonably detailed and quite independent test of the lattice dynamical models, we conclude that the present descriptions of vibrational properties of NaN3 should be adequate for most applications.