This paper proposes a rigorous method of three-dimensional slope stability analysis for convex slopes in plan view based on the upper-bound theorem of limit analysis approach and discusses about the effect of plan curvature on the stability of convex slopes. A rigid-block 3-D translational collapse mechanism is considered, with energy dissipation taking place along planar velocity discontinuities. This mechanism is optimized to obtain the minimum factor of safety for stability of the slope or to obtain the bearing capacity of rectangular foundations located on such slopes. based on comparisons with the known solutions, the method was generally found to be accurate in predicting the stability of convex slopes. The results show that the stability of convex slopes in plan view is more than the stability of slopes obtained by 2D analysis. Dimensionless diagrams for various parameters are also presented.