The extended KEM for rock slopes controlled by major geological discontinuities is studied. Numerical studies and verification indicate that the extended kinematical element method (KEM) can be used for analyzing all slopes where the limit equilibrium method (LEM) and Sarma method are applicable, and the factors of safety by the extended KEM are close to those by the two methods. However, the conventional Jennings method provides no information on the influence of the location of rock bridge. The extended KEM is more suitable in solving complex rock slope problems controlled by major geological discontinuities, allowing for a more realistic modeling of discontinuities. The discontinuity persistence plays an important role in the failure behavior of rock slope. Different discontinuity persistences result in different failure modes of a rock slope. The application of a large rock slope of open pit shows that the existence of major geological discontinuity has an adverse impact on the stability of slope.