A theory for calculating the ultimate strength of an infinite, brittle-matrix fiber composite is presented. At some stress level which is less than the ultimate strength, the composite is presumed to undergo multiple matrix cracking; this results in intact fibers spanning a series of roughly equally spaced matrix cracks. Subsequent damage in the form of fiber breaks is assumed to occur with the fiber strength being statistically distributed. With the use of some plausible assumptions, the spatial distribution of fiber breaks is computed and their effect on the subsequent load-carrying capacity of the composite is determined. The variables which most affect the ultimate strength are the interfacial shear stresses, which control load transfer near the matrix cracks and near the fiber breaks, and the fiber strength variability. A comparison with data in the literature indicates that a reliance upon simple rule-of-mixtures-type estimates of composite strength can be misleading.