Abstract: The safety factor of karst cave roof is defined as the ratio of actual shear strength parameter to critical failure shear strength parameter in this paper. Stability of karst cave roof was analyzed with strength reduction technique, elasto-plastic FEM and dichotomy. Then, not only the safety factor of karst cave roof with specific physics meaning can be obtained, but the overall failure process and the location of failure surface may also be determined at the same time, So the present method is obviously superior to those traditional methods. The calculated results of a few engineering examples prove that the proposed method is effective in analyzing the stability of karst cave under the pile tip.