Numerous observations and laboratory experiments suggest that elastic vibrations can significantly enhance transport of nonaqueous phase liquids (NAPLs) in porous media. Our analyses suggest that in the low-frequency range, capillary forces and nonlinear rheology of the fluid may be predominant mechanisms of vibratory stimulation. Consequently, a model of these mechanisms is built to explain the effect of sonic waves on fluid percolation. The model shows that the low-frequency elastic waves of relatively low intensity can significantly enhance the flow rate of a yield stress fluid under small external pressure gradients and aid in the mobilization of entrapped NAPL blobs by reducing the value of the threshold gradient needed to displace the fluid. We estimate the intensity of a sonic field to be used in the possible field implementation of this method to be in the range of 0.2--125 W/m2.