A fiber optic Michelson sensor was embedded in composite beams to sense the internal strain and points of failure of the composite structures. The bending deformation and matrix cracking were investigated by four-point bending tests of cross-ply composite beams with the embedded fiber optic sensor. The failure points of composite beams were detected by using both a PZT sensor and a fiber optic sensor in order to investigate the fiber optic failure signals. The failure due to matrix cracks in a composite beam was confirmed by the edge replica method. The digital processing of the fiber optic signal was carried out to determine the strains and failure points of composite beams. The failure points were observed from the processed failure signal by high-pass filtering. The initial failure strain of the composite beam was measured and processed from the fiber optic strain signal after low-pass filtering.