Toppling failure of a slope is defined as failure behavior accompanying the rotation of rock block which is different from other failure such as sliding along with discontinuities and so on. It generally occurs in the region that discontinuities were developed with inverse dip direction to a slope and it could play a critical role in judging stability of slope. In this study, the stability evaluation was performed about toppling failure on a jointed road cut-slope. To check the deformation behavior, numerical analysis is widely used. However common analysis programs are based on continuum model. Recently, many methods that discontinuity properties can be considered in continuum analysis are suggested. In this study, numerical analysis based on FEM(Finite Element Method) was performed using interface element applied in heterogeneous boundary to simulate effects of discontinuities.