Several challenges are encountered related to rock slope instabilities along national highways that traverse with steep topography. The Prithvi Highway, a critical highway that connects the capital of Nepal with the western and eastern regions, encounters significant slope instability. This is mainly the case in the segment of the Narayanghat-Mugling due to its steep terrain and geological conditions. This segment of road is under upgrading where widening of the carriageway is being made by cutting the topographic slope which causes exposure to the pre-existing discontinuities in the rock mass. This manuscript investigates the potential instability modes in one of the critical road segments. The geotechnical and engineering geological data have been established by field mapping and field tests. The stability assessment has been carried out using stereographic projection and numerical modeling using Finite Element Method (FEM) and Universal Distinct Element Code (UDEC). It is expected that the outcomes of this study will contribute to enhancing the nature of rock slope stability conditions and help to carry out engineering design in a sustainable way.