The leaky mode is a possible attenuation mechanism of seismic waves propagating along lamination in gas-hydrate-bearing sediment layers. This horizontal propagation attenuation mechanism occurs when a high-velocity layer is embedded in a low-velocity zone. This is a typical situation for gas hydrate occurrences. To quantify this attenuation mechanism, a 2D digital rock model based on the crosswell data of the Mallik 2002 Gas Hydrate Production Research Well Program is used. For simplicity, our elastic simulations exclude attenuation mechanisms like scattering loss or intrinsic absorption. We demonstrate that the leaky mode is a significant horizontal attenuation mechanism that cannot be neglected. The effective attenuation of gas-hydrate-bearing sediments is a combination of intrinsic and scattering attenuation by small-scale heterogeneties and the leaky mode.