In the present work a new theory of yielding and failure is derived for fiber composite materials. The importance of this general area is underscored by the high degree of activity that has been expended over the past 30 years or so in searching for the elusive best formulation. The difficulty of the search is evident from the multitude of empirical approaches that have been offered. The approach given here stresses the need to derive the governing forms from some basic physical postulations. In performing this derivation, a balance is sought between achieving the maximum generality and minimizing the number of materials parameters that must be experimentally evaluated for applications to any particular material system.