A new powerful numerical technique for investigating the failure of fiber reinforced composites is presented. The technique utilizes 3D lattice Green's functions to calculate load transfer from broken to unbroken fibers, and also includes the important effects of fiber/matrix sliding. The inherent flexibility of the technique in adjusting the spatial extent of load transfer allows for the study of many aspects of real composite failure processes which have been unobtainable to date. Using this technique, composite reliability, the influence of manufacturing defects on performance, and the overall optimization of composite performance can all be investigated in detail. Initial results using this approach show that load transfer and the existence of spatially-staggered fiber breaks play an important role in determining strength and toughness of composites. Furthermore, the critical configurations of fiber breaks that initiate catastrophic failure are complicated 3D objects and any single spatial plane is composed mainly of sliding fibers rather than broken fibers, with a few strong fibers intact within the critical defect.