The extent of finite soil deformation caused by liquefaction, flow and solidification, is addressed in this project. The study of the two- dimensional interactions between viscous two-component boundary layers and solidification waves, is undertaken for establishing criteria (based on soil properties and ground geometry) for predicting the extent of lateral spreading and flow failures. The study is based on a one-dimensional solidification process and a model constructed on the basis of two superimposed and interacting continua, the liquid and the solids. The investigation thus, is an extension and generalization of those findings to two dimensions, where the analysis focuses on the development of the two-dimensional constitutive relations between stress and strain rate in this bi-continuum framework. The results of this study will provide a more reliable way of predicting the extent of lateral spreading and flow failures in the event of a ground related hazard, and of estimating the damage potential to structures.