Overhead transmission lines play an important role on electric systems. Due to the high energy carried through those networks, failures on overhead lines can bring severe constraints on consumers supply, occasionally taking the form of blackouts in large geographic regions. Among the reasons of such failures is the breaking of electric cables caused by the fatigue originated from cyclic bending due to aeolian vibration. The large areas covered by overhead lines and the variety of climate, relief, vegetation and meteorological conditions under which they have to operate make it difficult to foresee the impact of wind Vibration measurements would allow anticipating the failure but conventional instruments depend upon electric transducers which, besides demanding a local source of energy (usually unavailable near overhead lines), suffer the influence of the high electric and magnetic fields around the energized cables. Optical fibers immunity against environments subjected to electrical and magnetic fields and the possibility of using low energy input signals offer the alternative of creating measuring instruments using Bragg gratings technique. This Master dissertation contributes with the development of a fiber Bragg grating biaxial accelerometer for measuring the vibration of overhead transmission line cables. Besides the theoretical and practical aspects related to the subject, the results of high precision calibration tests are discussed, together with other special tests which set the basis of the metrological evaluation and the establishment of the efficacy of the instrument.