Third-order time dependent perturbation theory is used to calculate the three-photon absorption coefficients of several direct-gap crystals. Both parabolic and nonparabolic energy band structures are employed. The intermediate states used in these calculations are the higher energy bands obtained from band structure calculations. The resulting three-photon absorption coefficients have the following frequency dependence. Initially the absorption coefficients increase with increasing energy, until a maximum is reached at a relatively low energy. On further increasing the photon energy the absorption coefficients decrease significantly. The behavior is qualitatively similar to the prediction of the Keldyoh formula, even though the magnitudes of the three-photon absorption coefficients obtained from the two calculations are different. The theoretical results for CdS at 1.06 μm agree well with the experimental data.