For the construction of railway embankments, geotechnical engineers pay special attention to slope stability studies. The factor of safety values plays a crucial part in assessing the safe design of slopes. The factor of safety values is used to determine how close or far slopes are from failing due to natural or man-made causes. The factor of safety is a numeric value to indicate the relative stability, it doesn’t tell about the actual risk level of any structure, but the reliability index and probability of failure quantify the risk level. The present study discusses the findings of a study to determine the factor of safety of an embankment of height 12.3 m by using Geo-studio 2012 software. In this article, the FRAGILITY curve for six different types of cross-sections was also developed i.e. the graph between the probability of failure ( ) and horizontal seismic coefficient ( ), for various values of (i.e. 0.1, 0.12, 0.144, 0.18, 0.2, 0.3, 0.4 and 0.5). It is observed from the developed FRAGILITY curve, as the value increases value decreases. A FRAGILITY curve can be used to calculate failure probability over a range of seismic zones, and for design purposes, a given seismic zone and probability of failure a unique reliable side slope is selected. Further, two machine learning (ML) models namely, Deep Neural Network (DNN) and Support Vector Regression (SVR) have been developed for the prediction of the factor of safety for different sides slope. Obtained correlation values (R) for SVR and DNN are approximately 0.95 and 0.82 respectively. From the help of the predicted factor of safety FRAGILITY curve against horizontal seismic coefficient is drawn for both SVR and DNN models, that for reducing the time of calculation and ease in working best result giving model will be suggested for further analysis of railway embankment.