The full set of third-order elastic constants of NaCl was measured and compared to some combinations of these constants that have been reported in the literature. The Cauchy relations were found to be reasonably well satisfied. For NaCl, C111 is large (of the order of 1013 dyn/cm2) and negative, C112 and C166 are smaller (of the order of 0.5×1012 dyn/cm2) and negative, and C123, C456, and C144 are small (of the order of 1011 dyn/cm2) and positive. It is shown that the closed-shell repulsive interaction between nearest and next-nearest neighbors gives the major contribution to the third-order elastic constants of NaCl and completely dominates the contributions to the fourth-order elastic constants. These fourth-order elastic constants are evaluated from the experimentally measured temperature coefficients of the second-order elastic constants. The Grüneisen parameter of 1.588 calculated from the measured second- and third-order elastic constants compares well with the Grüneisen constant of 1.64 obtained from thermodynamic measurements. Comparison of the third-order elastic constants obtained with linear combinations given by other methods shows that the two-specimen method used here gives results in fair agreement with one-specimen ultrasonic methods but not with optical methods.