A slow wave solution is identified for an infinite elastic medium intersected by a two-dimensional fluid channel. Because the wave speed is much lower than the medium's elastic shear wave, the response in the elastic medium is governed by elastostatics. The inertia of the wave is essentially focused in the fluid channel. Furthermore, wave damping is caused by fluid viscous friction on the channel's elastic walls. The solution is extended to the case of a distribution of fluid channels in and granular porous medium. The seepage channels would then represent a network of preferential flow paths. Therefore we would allow, in this case, the channel porosity to be different from the average granular porosity. For a strongly channeled seepage flow or for a low channel porosity the solution is shown to approach that of a single-channel solution, giving rise to a slow propagating wave mode. On the other hand, for weak channeling or nearly ''homogeneous'' seepage flow the solution is shown to reproduce Biot's (1956) critically damped wave of the second kind. It is proposed that the resonances observed by Foda and Tzang (this issue) are in the form of these strongly channeled wave modes. ¿ American Geophysical Union 1994