A slope stability limit analysis based on the translational failure mechanism is presented under typical uniformly-distributed loading and seismic loading conditions. The sliding body of slope is divided into arbitrary discrete blocks with inclined interfaces. Based on the upper-bound limit analysis method and nonlinear Mohr-Coulomb failure criterion, a general expression for safety factor Fs in state of critical failure is developed based on the multipoint tangent method and strength reduction method. In this expression, the inhomogeneity of normal stress in rock mass is considered. The upper bound solutions of the slope safety factor are obtained by applying a nonlinear sequential quadratic programming (SQP). The contrastive analysis shows that agreement with the previous results can be achieved by a relative error less than 3.565%, demonstrating the rationality and reliability of the proposed method. Meanwhile, the slope stability safety factors Fs calculated by multipoint tangent inclined slices method are smaller than those obtained by traditional single tangent inclined slices method, showing that multipoint tangent inclined slices method is a conservative and effective method for slope stability analysis. Parametric analysis indicates that the uniformly distributed loading, seismic loading and nonlinear parameters have significant effects on safety factor and the potential critical slip surface of the slopes. This paper provides a new approach to analyzing the slope stability by introducing the multipoint tangent method into the nonlinear Mohr-Coulomb failure criterion.