Recent sonic and seismic data in gas hydrate--bearing sediments have indicated strong waveform attenuation associated with a velocity increase, in apparent contradiction with conventional wave propagation theory. Understanding the reasons for such energy dissipation could help constrain the distribution and the amounts of gas hydrate worldwide from the identification of low amplitudes in seismic surveys. A review of existing models for wave propagation in frozen porous media, all based on Biot's theory, shows that previous formulations fail to predict any significant attenuation with increasing hydrate content. By adding physically based components to these models, such as cementation by elastic shear coupling, friction between the solid phases, and squirt flow, we are able to predict an attenuation increase associated with gas hydrate formation. The results of the model agree well with the sonic logging data recorded in the Mallik 5L-38 Gas Hydrate Research Well. Cementation between gas hydrate and the sediment grains is responsible for the increase in shear velocity. The primary mode of energy dissipation is found to be friction between gas hydrate and the sediment matrix, combined with an absence of inertial coupling between gas hydrate and the pore fluid. These results predict similar attenuation increase in hydrate-bearing formations over most of the sonic and seismic frequency range.