Abstract：The bifurcation phenomena，such as shear bands in geological structures，branching behaviors in rock tests and instability in geotechnical engineering，are described and some corresponding mechanisms are discussed. The theories widely applied in bifurcation analysis of localization in mathematics，structural mechanics analysis and geomaterial deformation are presented in detail. The processes for shear bands in loaded geomaterial to deform from toughness to brittleness，and then to lead to fracture of specimens，can not be well imitated by existing analysis methods. The plastic dilatable constitutive relationship together with symmetric group theories and asymmetric bifurcation analysis method are involved in the preliminary analysis. However，their effects are limited. The disturbed state concept proposed by Desai is introduced as a valuable way for the bifurcation analysis of material at the post-peak，with loading rate dependency，and under dynamic loading.
