Description: This report includes discussions of elastic and viscoelastic models for water‐saturated porous media, and measurements and computations of elastic constants including compressibility, incompressibility (bulk modulus), rigidity (shear modulus), Lamé's constant, Poisson's ratio, density, and compressional‐ and shear‐wave velocity. The sediments involved are from three major physiographic provinces in the North Pacific and adjacent areas: continental terrace (shelf and slope), abyssal plain (turbidite), and abyssal hill (pelagic). It is concluded that for small stresses (such as from a sound wave), water‐saturated sediments respond elastically, and that the elastic equations of the Hookean model can be used to compute unmeasured elastic constants. However, to account for wave attenuation, the favored model is ‘nearly elastic,’ or linear viscoelastic. In this model the rigidity modulus μ and Lamé's constant λ in the equations of elasticity, are replaced by complex Lamé constants (μ + iμ′) and (λ + iλ′), which are independent of frequency; μ and λ represent elastic response (as in the Hookean model), and iμ′ and iλ′ represent damping of wave energy. This model implies that wave velocities and the specific dissipation function 1/Q are independent of frequency, and attenuation in decibels per unit length varies linearly with frequency in the range from a few hertz to the megahertz range. The components of the water‐mineral system bulk modulus are porosity, the bulk modulus of pore water, an aggregate bulk modulus of mineral grains, and a bulk modulus of the structure, or frame, formed by the mineral grains. Good values of these components are available in the literature, except for the frame bulk modulus. A relationship between porosity and dynamic frame bulk modulus was established that allowed computation of a system bulk modulus that was used with measured values of density and compressional‐wave velocity to compute other elastic constants. Some average laboratory values for common sediment types are given. The underlying methods of computation should apply to any water‐saturated sediment. If this is so, values given in this paper predict elastic constants for the major sediment types.