We introduce a poroelasticity model that incorporates the two most important mechanisms of solid/fluid interaction in rocks: the Biot mechanism and the squirt‐flow mechanism. This combined Biot/squirt (BISQ) model relates compressional velocity and attenuation to the elastic constants of the drained skeleton and of the solid phase, porosity, permeability, saturation, fluid viscosity and compressibility, and the characteristic squirt‐flow length. Squirt‐flow length is a fundamental rock property that does not depend on frequency, fluid viscosity, or compressibility and is determined experimentally. We find that the viscoelastic response of many sandstones is dominated by the squirt‐flow component of the BISQ mechanism and that the viscoelastic properties of these rocks can be expressed through a single dimensionless parameter [Formula: see text] where ω is angular frequency, R is the characteristic squirt‐flow length, and κ is hydraulic diffusivity. The Biot mechanism alone does not give an adequate explanation of the observed velocity dispersion and attenuation, and the viscoelastic behavior of many sandstones.