Abstract Slope instability has been identified as one of the most natural and man-made disasters that can lead to the life of humans in danger and enormous loss of capital. The roads which pass on the hilly and mountainous terrains are frequently affected by slope failures since hilly and mountainous areas are characterized by variable topographical, geological, hydrological, and land-use conditions. Slope stability analysis was carried out using FEM (plaxis 2D) and LEM (slide software). The stability analysis covers both static and dynamic (in pseudo-static analysis) loading conditions on soil and rock material along selected critical slope sections. Two soil-critical slope sections and two rock-critical slope sections are analyzed in this study. The strength reduction method and method of the slice with Mohr–Coulomb model were used in FEM and LEM, respectively. The slope stability analysis was carried out for both dry and wet states of the soil and rock material along the critical slope sections (i.e., static dry, dynamic dry, static wet, and dynamic wet). The analysis result shows that the total displacement of the slope along soil critical slope section one is (0.58703, 0.58755, 2.35, and 2.38 m), along soil critical slope section two is (0.6574, 0.6621, 1.2841, and 1.2872 m), along rock-critical slope section one is (4.8624, 4.8672, 17.8463, and 17.8512 m) and total displacement along rock-critical slope section two is (3.8365, 3.8391, 11.437, and 11.6275 m) during static dry, dynamic dry, static wet, and dynamic wet loading conditions, respectively. In general, the result shows soil critical slope sections one and two are stable in dry conditions and unstable in wet conditions. Rock-critical slope sections are stable during the dry and wet states of the slope.