This thesis derives a Probability distribution function which expresses the expected length of discontinuous fiber segments in a uniaxially aligned fiber reinforced composite. The strength of elemental volumes of fiber, used in this derivation are inferred from 1ength versus strength tests.on individual fibers. The fibers are assumed to have statistically distributed flaws that allow characterization of fiber strength by a Weibull type equation. The probability distribution function is then used to compute the average fiber stress at composite failure. This allows calculation of composite strength by the well known law of mixtures. Composite strength determined by this method show good correlation with published experimental values for glass fiber composites. / Master of Science