Jointed rock slopes in the Himalayas present unique challenges for infrastructure development due to their complex geological setting and active tectonic dynamics. The slopes supporting the foundations of the Chenab railway bridge are an example of these challenges and are susceptible to various failure modes. This study proposes a comprehensive method to identify potential slope failure types in the jointed rock slopes of the Chenab railway bridge abutments. The method utilizes geological mapping data to reconstruct the jointed rock slopes. Kinematic analyses were performed to identify potential failure modes, including planar slides, wedge failures, and toppling. An equivalent continuum-based finite difference analysis was conducted to assess global stability, using the FLAC3D software with the Hoek–Brown material model to estimate displacements. The results from the kinematic analysis indicated that wedge failures are critical for the current study area. Support measures, specifically rock bolt forces, were estimated using wedge analysis for individual berms. Bolt forces were estimated for both static and pseudo-static conditions, and the maximum required forces were presented. The Mohr–Coulomb constitutive relation for the wedge-forming joints was applied, and an iterative approach was used to estimate the required rock bolt forces to achieve the target factor of safety values.