Abstract: Previous studies on the kinematical element method have mainly focused on analyzing the stability of soil slopes，whereas little attention has been paid to the rock slope stability problem. Rock mass usually contains various discontinuities of different characteristics that play a dominant role in the mechanics behavior of rock slope. However, conventional methods are not applicable to analyze the combination failure on the rock bridge and the discontinuities. To solve the problem of rock slope stability controlled by discontinuities，vertex kinematic constraint conditions of the plastic sliding zone in the rock bridge and on the discontinuity were investigated. Kinematical element formulations were derived to calculate the factor of safety of the rock slope containing discontinuities. The improved kinematical element method was presented. Classic examples were given for demonstrating the validity of the results obtained by the improved kinematical element method. The results show that the location of rock bridge，the discontinuity persistence and the discontinuity inclination are found to have the dominant effects on the mechanics behavior of the rock slope. The factor of safety with the rock bridge near the slope toe is larger，whereas the Jennings method provides no information on the influence of the location of rock bridge. A high discontinuity persistence causes a rock slope to fail in the combined failure mode with a lower factor of safety，whereas a low discontinuity persistence leads to the failure of intact rock with a higher factor of safety. A horizontal or sub-vertical/vertical discontinuity leads a slope to fail in a mode of cutting through the discontinuity with a higher factor of safety，whereas other discontinuity inclinations cause the combined failure with a lower factor of safety. The proposed method can effectively evaluate the stability state of rock slope, and can be applied in similar practical engineering.