Fiber breakage occurring in fiber bundles of plain-woven glass fabric composites is investigated under tension/shear biaxial cyclic stress. The experimental results show an existence of the strong effect of biaxial stress ratio on fiber breakage and its accumulation. Under pure tension (uniaxial) loading, the variation of fiber breakage ratio with respect to loading cycles is divided into two stages in the longitudinal fiber bundles. In the first stage, the fiber breakage scarcely occurs. In the final stage, fibers in a fiber bundle are broken remarkably. Under the biaxial cyclic stress, the fiber breakage in the longitudinal fiber bundle is observed in initial fatigue stage. In the case of the biaxial stress with large shear stress component, the fiber breakage is also observed in the transverse fiber bundle. The fiber breakage is accelerated by the combined stress with large shear stress component, which is called the shear constraint effect.