The dynamics of cohesive mud under wave action is important to the geological processes along some coastlines. Becaue of the complex rheological properties there have been vastly different models for predicting the effect of mud on wave attenuation. This paper focuses on a non-Newtonian behavior of highly concentrated mud, whereby shearing strain occurs only if the shear stress exceeds a certain threshold called the yeild stress. The wave-induced motion in a thin mud layer beneath a clear water layer is studied. There are circumstances in which the yield stress is dominant and acts like a Coulomb friction. Mud motion can change from continuous to intermittent as the wave attenuates. The effects of the non-Newtonian behavior on wave damping are compared to other more common causes of dissipation. ¿ American Geophysical Union 1987