Relatively unconsolidated sediments of low rigidity μ are common in oceans. Shear modes of low velocity cs(cs≲100 ms−1) then exist in sea floor sediments, as well as slow boundary waves of velocity v<cs at the water–sediment interface (Stoneley modes). Both have been observed in shallow water experiments at frequencies in the 1–5 Hz band [Rauch, Bottom‐Interacti ng Acoustics (Plenum, New York, 1980)]. In poorly consolidated sediments of this kind ( μ<109 dyn cm−2) gravity and other stresses introduce small corrections to the propagation velocities. The role of gravity is of two sorts. On the one hand it introduces buoyancy forces and internal gravity waves—these are negligible for frequencies above 10−1 Hz; on the other, it introduces hydrostatic stresses which primarily affect the velocity of shear modes in the sediment—leading to corrections of order ρgz/μ (for an overburden of height z in a sediment or sediment+water column of mean density ρ). While the latter measurably affects propagation speeds in sediments, it is an isotropic effect which, in practice, finds itself lumped with other mechanisms of velocity stratification. Interesting and in principle more easily diagnosed in experiments are the effects of anisotropic stress fields—e.g., tensions and compressions associated with gravity slumping mechanisms on slopes and, for deeper and somewhat more consolidated sediments, with forces of local origin such as island loading or tectonic stresses. These can introduce measurable anisotropies into the propagation of various low‐frequency bottom associated modes.