During an earthquake loose soil materials such as mine tailings may liquefy, resulting in severe damage or failure of the tailings dam. In this paper, a mechanics based total stress analysis approach is presented which uses the finite difference geomechanics modeling program FLAG to model the triggering of soil liquefaction and the resulting large displacement. In the approach, an earthquake motion is assigned to the bedrock surface under a dam and the induced cycles of shear stress are counted in each element of the model. When sufficient cycles have accumulated to trigger liquefaction in an element, the stress state in the element is set to that of a fluid and the strength and stiffness parameters are set to their post-liquefaction values. As earthquake shaking continues, additional elements may liquefy and deform in their attempt to mobilize resistance and return the system to dynamic equilibrium. In this way, the magnitude and pattern of displacements is predicted. This approach is used to back-analyze the response of two tailings dams at the Mochikoshi gold mine in Japan in 1978, when a magnitude 7.0 earthquake liquefied the tailings. The approach correctly models the failure of one dam during the main earthquake event, and also correctly simulates that a second dam deformed but did not fail during the main event. This result helps to verify the analysis approach, and lends confidence to applying the method for predicting earthquake response of an existing or planned tailings dam. A comparison of potential remediation measures to seismically upgrade a tailings dam is presented, where it is shown that a very significant construction cost saving can be realized if the proposed method is used rather than older simpler methods which make conservative assumptions.