This paper proposes an intelligent system for solving the fault diagnosis problem in electrical power transmission system, involving substation equipments and transmission lines. The proposed methodology is based on Bayesian Networks and this paper is focusing only on the failures related to transmission lines. The fault diagnosis in power transmission systems is a complex problem and its solution usually needs a great deal of expertise and experience related to equipments, transmission systems and failures modes. The developed system allows not only the definition of the most probable cause of a detected failure, but also the prognosis of possible failures, when some evidences of equipment status or causes are known. Validation tests were performed with this computational model, considering realistic data from a Brazilian transmission utility. The tests have demonstrated the effectiveness of this approach, confirming it as a promising computational tool to the maintenance engineers.