A model for a saturated, porous elastic medium containing bubbles of gas [J. Acoust. Soc. Am. 73, 409–417 (1983)] has been combined with a model for a bubbly liquid with a bubble population whose radii vary continuously over a known distribution [J. Acoust. Soc. Am. Suppl. 1 88, (1990)] to obtain an acoustical model for saturated sediments containing a distribution of bubble sizes. The dispersion relation has been obtained and the phase velocity and attenuation have been calculated as functions of frequency for several distributions of bubble sizes. The presence of a distribution of bubble sizes tends to smooth the effects of bubble resonance on the phase velocity and attenuation in comparison with a single bubble size, but the main qualitative effects of bubble resonance remain intact.