Biot's linear model of stress-wave propagation in a fluid-saturated elastic framework is combined with a linear theoretical description of an inelastic frame to describe fluid-saturated media in terms of a composite model. The composite model, the Constant Q (CQ) model, assumes an inelastic frame with frequency-dependent complex elastic moduli and results in a frame response that is causal with Q exactly independent of frequency.The influence of frame inelasticity on the composite-model Type I (compression), Type II, and shear-wave attenuation response is found to be greatest for high and low frequencies, considering a frequency range of 10-10 7 Hz. The model is most sensitive to variations in permeability and pore-size parameter for both attenuation and phase-velocity responses. Parameter variations showed little effect on shear-wave attenuation for a fine to coarse sand-size frame matrix, indicating a fluid mechanism is responsible for the influence seen in Type I and Type II attenuations.The CQ model results fit the experimentally measured values of Type I attenuation and velocity for a fully saturated fine-grained frame material (clay-silt size grains) and a fully saturated coarse-grained frame material (fine to coarse sand-size grains). For Type I velocity, the experimentally observed dispersion clearly distinguishes the CQ model as superior to composite models that include a nondispersive frame, since such models predict very little dispersion due only to interpore fluid mechanisms.