A new two-phase theory employing a nonequilibrium relation between interfacial surface energy, pressure, and viscous deformation <Bercovici et al., this issue>provides a model for damage (void generation and microcracking) and thus a continuum description of weakening, failure, and shear localization. Here we demonstrate applications of the theory to shear localization with simple shear flow calculations in which one phase (the matrix, representing, for example, silicate) is much stronger (more viscous) than the other phase (the fluid). This calculation is motivated as a simple model of plate boundary formation in a shear zone. Even without shear the two phases eventually separate due to gradients in surface tension. However, the influence of shear on phase separation is manifest in several ways. As shear velocity increases, the separation rate of the phases increases, demonstrating a basic feedback mechanism: Accumulation of the fluid phase causes focused weak zones on which shear concentrates, causing more damage and void generation and thus greater accumulation of fluid. Beyond a critical shear velocity, phase separation undergoes intense acceleration and focusing, leading to a tear localization in which the porosity becomes nearly singular in space and grows rapidly like a tear or crack. At an even higher value of shear velocity, phase separation is inhibited such that shear localization gives way to defocusing of weak zones suggestive of uniform microcracking and failure throughout the layer. Our two-phase damage theory thus predicts a wide variety of shear localization and failure behavior with a continuum model. Applications of the theory to various fields, such as granular dynamics, metallurgy, and tectonic plate boundary formation are numerous. ¿ 2001 American Geophysical Union