Slope Stability is one of the crucial topics in geotechnical engineering to be investigatedrnwell because oftentimes slope exists naturally or formed artificially during construction ofrnvarious civil engineering structures which needs to be at equilibrium. For that matter, therernare various methods of analysis. For the last couple of decades, it is observed hard forrnEngineers to use Probabilistic Slope Stability Analysis due to many reasons. But theserndays, technological advancements which led to having more rigorous software packagesrnmade it be possible to use in the analysis and its merit. The aim of this thesis is to showrnthe use of more reliable method of slope stability analysis for hypothetical back slopes inrnAddis Ababa where red clay soil is dominant and that is achieved by comparing methodsrnbased on a factor of safety, probability of failure, and reliability index. rnLimit Equilibrium Method (LEM) and Numerical Method are used for this purpose. Bothrndeterministic and probabilistic analyses are carried on by modeling seven slope geometriesrnwith different input parameters from Addis Ababa ring road III project and hypotheticalrnslopes using a two-dimensional Slope Stability analysis software called SlideV6.0. ArnGlobal Minimum type of analysis are carried on by using the Slide software. For finiternelement analysis and probabilistic finite element analysis, RS2 software from Rocsciencernis used. Uncertainty is accounted for in a better way in probabilistic analysis by definingrnparameters as a random variable in link with other features. rnIt is shown by this study that, Probabilistic Finite Element Analysis (PFEA) seeks out thernmost critical slip surface than that of the finite element method. In addition, even if thernfactor of safety found from the deterministic analysis is greater than one still a probabilityrnof failure is observed. Moreover, it is attested that the factor of safety is not the onlyrnmeasure for slope stability, but other measures exist while using probabilistic analysis.