Understanding three-dimensional (3D) slope deformation and failure mechanism and corresponding stability analyses are crucially important issues in geotechnical engineering. In this paper, the mechanisms of progressive failure with thrust-type and pull-type landslides are described in detail. It is considered that the post-failure stress state and the pre-peak stress state may occur at different regions of a landslide body with deformation development, and a critical stress state element (or the soil slice block) exists between the post-failure stress state and the pre-peak stress state regions. In this regard, two sorts of failure modes are suggested for the thrust-type and three sorts for pull-type landslides, based on the characteristics of shear stress and strain (or tensile stress and strain). Accordingly, a new joint constitutive model (JCM) is proposed based on the current stability analytical theories, and it can be used to describe the mechanical behaviors of geo-materials with softening properties. Five methods, i.e. CSRM (comprehensive sliding resistance method), MTM (main thrust method), CDM (comprehensive displacement method), SDM (surplus displacement method), and MPM (main pull method), for slope stability calculation are proposed. The S-shaped curve of monitored displacement vs. time is presented for different points on the sliding surface during progressive failure process of landslide, and the relationship between the displacement of different points on the sliding surface and height of landslide body is regarded as the parabolic curve. The comparisons between the predicted and observed load–displacement and displacement–time relations of the points on the sliding surface are conducted. The classification of stable/unstable displacement–time curves is proposed. The definition of the main sliding direction of a landslide is also suggested in such a way that the failure body of landslide (simplified as “collapse body”) is only involved in the main sliding direction, and the strike and the dip are the same as the collapse body. The rake angle is taken as the direction of the sum of sliding forces or the sum of displacements in collapse body, in which the main slip direction is dependent on progressive deformation. The reason of non-convergence with finite element method (FEM) in calculating the stability of slope is also numerically analyzed, in which a new method considering the slip surface associated with the boundary condition is proposed. It is known that the boundary condition of sliding surface can be described by perfect elasto-plastic model (PEPM) and JCM, and that the stress and strain of a landslide can be described properly with the JCM.