The statistical aspects of the failure of large 3-D unidirectional fiber reinforced composites are studied numerically and analytically. A 3-D lattice Green's function model is used to calculate the stress field, damage evolution, and Failure in composites under ''Local Load Sharing'' (LLS) conditions in which the stress from broken fibers is transferred predominantly to the nearby unbroken fibers. Failure by local accumulation of a critical amount of damage, and the associated decrease in ultimate strength with increasing composite size, is explicitly demonstrated. Weakest-link statistics are then employed to investigate size effects and reliability. An intrinsic ''link'' in LLS is found which has the same Gaussian distribution function for strength as a bundle in Global Load Sharing (GLS) (no local stress concentrations) of the same size. The size of the link is found to be comparable to the critical cluster of fiber damage observed in the simulations. Then, using known results for the GLS probability distribution function, analytic asymptotic results for the strength and reliability of large composites in LLS are derived. The strength distribution shows excellent agreement with the Monte Carlo simulation results for both the median strength and high reliability tail of the distribution. The implications of these results on the expected strength and reliability of moderate-size composites components is discussed, with applications to a Ti-MMC and a SiC/SiC CMC. Finally, the application of these results to modeling of composite failure by the Finite Element Method is presented. (C) 1997 Elsevier Science Ltd.