The measured amplitude A of ultrasonic pulses in intact and fractured samples of water-saturated gabbro and granite is observed to decrease as the permeability &kgr; increases according to the proportionality A∝&kgr;-1/2. This relation is predicted by Biot's theory of elastic waves in fluid-saturated porous media and, therefore, suggests that Biot's attenuation mechanism may play a significant role in low porosity materials at ultrasonic frequencies. The evidence is not conclusive. The limited data set studied here is also consistent with correlations of the form A∝&kgr;-&Egr; where 0.2<&Egr;<0.6. Nevertheless, the observed correlations may still provide a means for monitoring changes in permeability of low-porosity underground repositories of radioactive waste.