Gravity waves propagating on the surface of ice-covered water of finite depth are considered. The ice layer is viewed as a suspension, with an effective viscosity much greater than that of water and a density slightly less than that of water. It is treated as a viscous liquid, and the water beneath it is treated as an inviscid liquid. The linearized motion of gravity waves is analyzed for this two-layer model, and the dispersion equation is obtained. It is solved numerically for waves of any length. It is also simplified for waves short compared to the layer thickness and for waves long compared to the layer thickness. This equation yields dispersion and strong attenuation, both of which depend upon the effective viscosity of the suspension. ¿ 1998 American Geophysical Union