The vast majority of slopes, both natural and constructed, exhibit a complex geometric configuration and three-dimensional (3D) state, whereas slopes satisfying the assumption of plane strain (infinite length) are seldom encountered. Existing research mainly emphasizes the 3D dimensions and boundary effect in slope stability analysis; however, the effect of complex geometric ground configuration on 3D slope stability is rarely reported. In this paper, an elastoplastic finite-element method using strength-reduction techniques is used to analyze the stability of special 3D geometric slopes. A typical 3D slope underlain by a weak layer with groundwater is described to validate the numerical modeling, safety factor values, and critical slip surface for the 3D slope. Furthermore, a series of special 3D slopes with various geometric configurations are analyzed numerically, and the effects of turning corners, slope gradient, turning arcs, and convex- and concave-shaped surface geometry on the stability and failure characteristics of slopes under various boundary conditions are discussed in detail.