We offer an effective-medium model for estimating the elastic properties of high-porosity marine calcareous sediment and diatomite. This model treats sediment as a pack of porous elastic grains. The effective elastic moduli of the porous grains are calculated using the differential effective-medium (DEM) model, whereby the intragranular ellipsoidal inclusions have a fixed aspect ratio and are filled with seawater. Then the elastic moduli of a pack of these spherical grains are calculated using a modified (scaled to the critical porosity) upper Hashin-Shtrikman bound above the critical porosity and modified lower (carbonates) and upper (opal) Hashin-Shtrikman bounds below the critical porosity. The best match between the model-predicted compressional- and shear-wave velocities and Ocean Drilling Program (ODP) data from three wells is achieved when the aspect ratio of intragranular pores is 0.5. This model assigns finite, nonzero values to the shear modulus of high-porosity marine sediment, unlike the suspension model commonly used in such depositional settings. The approach also allows one to obtain a satisfactory match with laboratory diatomite velocity data.