The complete set of third-order elastic constants for single crystals of NaF was determined from the hydrostatic-pressure and uniaxial-stress derivatives of natural sound velocities measured with a two-crystal ultrasonic-interference technique. There appeared to be no dislocation motion during the uniaxial measurements since changes in the natural sound velocities with stress were linear, and data recorded before and after a γ irradiation agreed within experimental error. The Cauchy relations were not satisfied revealing that noncentral forces between the ions are appreciable. Calculations of the elastic constants were carried out according to the Born model. The high-temperature Grüneisen constant and thermal-expansion coefficient were determined from the elasticity data and the latter compared with experimental results.