The effects of holes and notches on the ultimate tensile strength of a unidirectionally reinforced titanium matrix composite have been examined. During tensile loading, a narrow plastic strip forms ahead of the notch or hole prior to fracture, similar to that observed in thin sheets of ductile metals. Examination of the fibers following dissolution of the matrix indicates that essentially all the fibers within such a strip are broken prior to catastrophic fracture of the composite. The trends in notch-strength have been rationalized using a fracture mechanics-based model, treating the plastic strip as a bridged crack. The observations suggest that the bridging traction law appropriate to this class of composite is comprised of two parts. In the first, the majority of fibers are unbroken and the bridging stress corresponds to the unnotched tensile strength of the composite; in the second, the fibers are broken and the bridging stress is governed by the yield stress of the matrix, with some contribution derived from fiber pullout. This behavior has been modeled by a two-level rectilinear bridging law. The parameters characterizing the bridging law have been measured and used to predict the notch strength of the composite. A variation on this scheme in which the fracture resistance is characterized by an intrinsic toughness in combination with a rectilinear bridging traction law has also been considered and found to be consistent with the predictions based on the two-level traction law.