The aim of this thesis is the theoretical calculation of the minimum safe distance of a settlement slope in case of failure and the drawing of conclusions about the accuracy of the results from the use of the methods that will be applied. For this purpose, the slopes of two mines (Northern Mathiatis Mine, Corta Atalaya) were studied with three methods in order to calculate the safety factor for various combinations of cohesion values and friction angles, and then to calculate the failure distances (lengths) (crest-crack distance) up to two failures. In the Mathiatis mine, the limit analysis method based on the upper limit theorem was applied by determining the kinematic mechanism of the slope and calculating the work produced during sliding, while the energy consumed is calculated based on the theory of ideal plasticity and the Mohr-Coulomb criterion. In the Corta Atalaya mine, the methods of circular failure diagrams and the simplified Bishop strip method were applied. The method of circular failure diagrams was studied from the book “Rock Slope Engineering” by Wyllie & Mah with the conditions that the slopes are homogenized and the circular slip surface passes through the foot of the slope. To solve the simplified Bishop method, the free program HYRCAN with Mohr-Coulomb criterion was used. In all methods, the SDs were calculated and for those whose result was less than unity, the horizontal distance of the first and second failure was calculated, which were then summed to calculate the total failure distance. From the application of the methods, the minimum distances according to which a settlement is safe were calculated in both cases.Keywords: Safety factor, failure, settlement, slope, horizontal distance crest-failure, open pit exploitation