Biot slow-wave effects in layered materials have been studied previously by Pride et al. (2002) and many others found in their references. The present work is motivated by the desire to understand how fluids interacting with common poroelastic systems may create viscous attenuation in partially saturated (and especially in patchy saturated) cylinders. These effects can then be observed in the attenuation of extensional and torsional waves. There are large quantities of such data already available, and one thrust of our future work will be to reanalyze these data in light of the methods developed here. We have concentrated on analysis of the wave velocities here, as this is clearly the first essential step in the overall analysis of these problems.