Abstract：The spatial development of a single shear band in saturated brittle rocks for anti-plane shear deformation is investigated. The saturated rock is taken as a solid-liquid two-phase medium. Perturbation method is used to analyze the stability conditions. The solid medium is taken to be elasto-plastic，and is the function of strain，strain ratio and pore pressure or stress history. The solid medium is compressible，and the liquid satisfies the Darcy law. The inertial effects and the force between two media are considered in the analysis. It is shown that，if the angle between the proportional loading path and the direction of the localization is p/2，then the deformation is stable. This agrees well with the case of neutral loading. The case that Dq is more than p/2 corresponds to elastic unloading，while the one that Dq is less than p/2 corresponds to loading and the instability develops the fastest when Dq is equal to zero. Positive solutions for a require that the rate of pore pressure softening exceeds that of strain hardening. Under two limit conditions，namely，long wave and short wave，the saturated brittle rock is stable.
