Abstract：Based on Drucker-Prager yield criterion，analytical solution of discontinuous bifurcation of materials is formulated under plane strain condition，and the bifurcation condition is implemented in the self-developed elasto-viscoplastic adaptive finite element analysis software AFEAS. Elasto-viscoplastic constitutive relation and solution program of localization are given to trace inception and progression of localization zone of rock mass. Slope stability plays critical roles in many projects，studying failure mechanism of slopes has important significance of theory and application. According to Bifurcation theory，slope instability is studied as a bifurcation phenomenon. Compared with traditional yield damage theory，bifurcation theory has more advantages—process of inception and progression of localization zone can be traced，the collapse load-carrying capacity of the slope can be determined and more definite failure zone can be provided for slope stabilization. A numerical example of slope instability is studied and shows the rationality of the theory and software.
