Current dominant methods for slope stability analysis are the limit equilibrium method and the strength reduction method. Both methods are based on the limit equilibrium conditions. However, the limit equilibrium methods are limited to the rigid body assumption, while the strength reduction method is computationally expensive and has convergence issues due to its non-linear iterative computations. In this paper, we propose a current stress-based search algorithm to directly obtain the critical slip surface and the safety factor. The numerical manifold method, which unifies the continuum and discontinuum analysis problems, is used for stress analysis to obtain the stress distribution of soil slopes or rock slopes cut by joints. Based on the stress results obtained, a graph theory is used to convert the solution of the critical slip surface to a shortest path problem, which can be directly solved by the Bellman-Ford algorithm. The proposed method couples the numerical manifold method and the graph theory allowing for stability analyses of both rock and soil slopes within the same framework. The method completely removes the computational effort needed for iterations in the strength reduction method as well as eliminating the rigid body assumptions in the limit equilibrium method.