Buckingham’s grain‐shearing (GS) theory of wave propagation in saturated granular materials predicts a sound speed showing weak dispersion and an attenuation that scales essentially linearly with the frequency. Measurements of the dispersion curves made during the SAX99 experiment in the Gulf of Mexico match the GS theory at higher frequencies, above 10 kHz, but show a lower sound speed and a higher attenuation than predicted by the GS theory at lower frequencies. A generalized version of the GS theory has now been developed, designated the VGS theory, which takes into account the effective viscosity of the molecularly thin layer of pore fluid between contiguous grains. In effect, the viscosity of the pore fluid limits the degree strain‐hardening that occurs as grains slide against one another. The resultant VGS dispersion curves are the same as those of the GS theory, except for the appearance of a simple algebraic function that has an effect only at frequencies below about 10 kHz. This low‐frequency function gives rise to VGS compressional‐wave dispersion curves that match the sound speed and attenuation measurements made during SAX99 across the frequency band from 1 kHz to 400 kHz. [Research supported by ONR.]