In the previous limit equilibrium stability analyses of concave and convex slopes, the kinematic constraints are not considered in the generation of slip surfaces. To tackle this problem, this technical note proposes a method to compute safety factors of concave and convex slopes, combining the simplified Bishop method with an adaptive “point-by-point” technique. Through the adaptive “point-by-point” technique, the failure surfaces of slopes are linked by numerous lines that connect two neighboring discretized points, at which the velocity compatibilities are strictly satisfied. Stress analyses are made for the vertical discretized slices where the lateral pressure on the interface between soil slices is represented by the Rankine active earth pressure. Based on the simplified Bishop method and the strength reduction method, the safety factor and failure surfaces of concave and convex slopes are derived, which are verified by numerical simulations. Comparative outcomes show that the results would be closer to those of numerical simulations if the strength reduction is made for the Rankine active earth pressure on the interface between soil slices. And the proposed discretized slip surface considering kinematic constraints is more consistent with the shear bands by numerical simulation, as compared with the circular arc slip surface. Under homogeneous soil conditions, the proposed discretized slip surface can degenerate into a logarithmic spiral.