Rock masses usually includes diverse types of discontinuities including faults, joints, bedding planes and shear zones. It is claimed that the discontinuities are the most leading attributes controlling stability of surface structures. Regarding concrete arch dams, strength and deformation properties of foundations and abutments are the most important factors to be considered in choosing the type of dam. Hence, studying the strength properties and the location of dams from the abutments are as high importance. The aim of this study is to investigate the stability of Pir-Taghi double-arch concrete dam using numerical modeling and analytical methods. By means of studying the behavior of discontinuities, unstable wedges are identified using Mohr-Coulomb criteria and critical wedge stability analysis is performed acquiring numerical modeling. However, considering the changes in cohesion and friction angle, the factor of safety for critical wedge is determined. Stability analysis is conducted and factor of safety for critical wedge is determined using both Londe and Hoek - Bray approaches. Comparing the results revealed by numerical modeling methods and Hoek - Bray and Londe approaches, there is a significant correlation between the results. Finally, assuming the assured stability of the rock mass, the studied structure is assumed to be a fortified structure