Relaxation models fail to predict and explain loss characteristics of many viscoelastic materials which follow a frequency power law. A model based on a time-domain statement of causality is presented that describes observed power-law behavior of many viscoelastic materials. A Hooke's law is derived from power-law loss characteristics; it reduces to the Hooke's law for the Voigt model for the specific case of quadratic frequency loss. Broadband loss and velocity data for both longitudinal and shear elastic types of waves agree well with predictions. These acoustic loss models are compared to theories for loss mechanisms in dielectrics based on isolated polar molecules and cooperative interactions.