Abstract: The site of Five-hundred-meter Aperture Spherical radio Telescope is located in karst depression, and the depression slope shape after excavation is like a spherical cap shape slope which belongs to an axisymmetric circular concave slope. The slope is composed of cemented soil-rock mixture and limestone. The slope is locally stable, but the stability of slope in a whole is still unknown. At present, evaluation of the slope stability in a whole is usually using the limit equilibrium method which is based on plane strain, and error arises in the evaluation results of the axisymmetric circular concave slope because of ignoring the slope shape. To eliminate the error, the slide body of the axisymmetric circular concave slope is divided into many annulus slices in the study, the anti-slide capacity of annulus slices axial force is considered and the improved limit equilibrium method which is suitable to the axisymmetric circular concave slope is proposed. The improved simplified Bishop method is verified with the numerical analysis method. The results show that the safety factor of the improved simplified Bishop method is a little larger than that with the traditional calculation method, and the safety factor of the improved simplified Bishop method is close to the numerical method result. The safety factor equation of the axisymmetric circular convex slope is given, and the results show that the stability of the axisymmetric circular convex slope is close to that of the ordinary slope. The above two calculation methods may provide new ways to evaluate the stability of slope with similar slope shape.