A new three-dimensional (3D) slope stability analysis method is developed based on two-directional moment equilibrium. This method calculates not only the safety factor but also the possible direction of sliding for semispherical and composite failure surfaces. As a result, the possible errors associated with assuming a plane of symmetry in 3D stability analyses are eliminated. Another advantage of the new method is to eliminate the tedious work on the coordinate transformation prior to the analysis. Two examples of symmetrical failure surfaces are used to verify the basic formulation in the present study. Three additional examples further demonstrate the applicability of the proposed method in analyzing 3D asymmetrical failure surfaces. An analysis on a slope, subject to asymmetrical excavation unloading and geological conditions, shows that using the method of one-directional moment equilibrium may give an overestimated safety factor of the slope.