A framework is developed for estimating the volume fraction of fat in steatotic livers from viscoelastic measures of shear wave speed and attenuation. These measures are emerging on clinical ultrasound systems' elastography options so this approach can become widely available for assessing and monitoring steatosis. The framework assumes a distribution of fat vesicles as spherical inhomogeneities within the liver and uses a composite rheological model (Christensen 1969 J. Mech. Phys. Solids 17 23-41) to determine the shear modulus as a function of increasing volume of fat within the liver. We show that accurate measurements of shear wave speed and attenuation provide the necessary and sufficient information to solve for the unknown fat volume and the underlying liver stiffness. Extension of the framework to compression wave measurements is also possible. Data from viscoelastic phantoms, human liver studies, and steatotic animal livers are shown to provide reasonable estimates of the volume fraction of fat.