A structural and engineering geological study of rock slope stability was carried out in six stations that lie in the Southwest of Baranan mountain, along Sirwan road. The rock slopes and discontinuities were surveyed at each of these stations, and the relationships with failures were determined. The slopes were classified on the basis of (Al-Saadi, 1981), and the rocks were described in engineering terms according to (Anon, 1972) and (Hawkins, 1986), Stereographic projection was made using software (GEOrient 9.5.0) to represent the field data that were recorded in order to understand the situation in the six stations (sites) that were chosen along Sirwan road near Darbandikhan dam, the failures' types were recorded during field study were rock fall, toppling, and sliding. The study also revealed that the factors affecting slope stability in the study area were slope angle, height, dip of strata, and discontinuities. The laboratory test of the rock samples (point-load test) showed that the average value of compressive strength of the rock for the study area is about 181.29 MPa.Some measures are proposed to stabilize the slopes in the mentioned stations including; the removal of blocks liable to toppling in the critical cases (sites 2 and 6), casing the slopes with covenant materials such as concrete (site 4) and gabions (sites 2 and 6), with construction of retaining walls and digging of protective trenches to protect the slopes and reduce their hazard on the road (site 1, 3, and 5).