The attenuation of normal modes in a two‐layered fluid medium due to absorption in the lower semi‐infinite layer is calculated under the assumption that this absorption is small. The result obtained gives the attenuation coefficient for each mode as the product of the absorption coefficient for plane waves in the absorbing layer and a dimensionless function of wavelength and layer depth. Curves of this dimensionless function are plotted for the first five modes in cases typical of propagation in shallow water over a sand and a mud bottom. The results indicate a very rapid decrease in attenuation as the frequency rises above the cut‐off frequency, where it is just equal to the bottom absorption. At higher frequencies the attenuation varies as (n2λ3/H3)α, wherenis the mode number, λ the wavelength,Hthe water depth, and α the absorption coefficient in the bottom (α may itself be a function of frequency). The latter result is also derived by a less rigorous method.