This thesis concentrates on the frequently failures occurred in the high pressure compressor blades of the HESA Power Plant in Isfahan. These blades belong to the 9 th stage of the compressor and their material is titanium alloy Ti-6Al-4V. In addition, all reported failures are related to the root part of the blades. Finite element method and software ANSYS was applied for the force analysis of the blades. These simulations were carried out at both 2D and 3D dimensions under contact stresses-which have the basic role on the failures-, centrifugal and aerodynamic forces. The results showed a high stress gradient and Von Misses stress concentration on the edge of contact and it can be concluded that this area is prepare for the crack initiation. For investigating the stress condition of the blade and its root after initiation of cracks, another simulation was carried out. In this analysis, different initial cracks were created on the geometry of the blade root by using a code which was wrote in ANSYS software. It was shown that in all cracked root, there is a high gradient and Von Misses stress concentration along the crack front which is higher than the fretting fatigue threshold stress of Ti-6Al-4V. It can prove that created cracks in this area can propagate by the mechanism of fretting fatigue. The stress intensity factors of the cracked roots were also evaluated along the crack front. It was shown that although all fracture modes are interfered in the blades failures, the mode I is very strong and has the chief part on the fractures. In addition, different metallurgical tests were carried out on the broken blade sections. By these tests the Fretting Fatigue was introduced as mechanism of crack initiation and the crack initiation points were also detected which exactly were the same point by the maximum stress concentration on the edge of contact of the blade. Thus, the results of metallurgical tests can prove those ones obtained by the numerical simulations.