The determination of the maximum safe-slope angle with a planned slope height is a critical issue in slope design and construction. In this study, to overcome the drawbacks of the rule of thumb and trial-and-error methods, the optimization of slope angle is treated as a root-finding problem. The kinematical element method (KEM) within a rigorous theoretical framework is used to solve this problem using the modified false-position method. The critical noncircular-failure surface and the associated minimum factor of safety are located using the KEM. A rock slope with planar failure is given for demonstrating the validity of this method. The result shows that the maximum safe-slope angle obtained using the KEM is consistent with the analytical solution. The method proposed in this study has a satisfactory convergence speed. In addition, a bench-shape fill slope in an iron and steel base is used as a case study. The maximum safe-bench face angle of the fill slope, under self-weight condition, is 41.43°, and it decreased by 17% due to seismic loading. Finally, the effect of the slope height on the maximum safe-slope angle is analyzed, and strong correlations that display an exponential function are found. The critical failure surface associated with the maximum safe-slope angle becomes deeper as the slope height increases.