The paper presents the formulation of boundary value problems of determining the stress-strain state of a unidirectional composite reinforced by fine fibers. The stress state is the result of uneven shrinkage fibers. The problems for composites with elastoplastic, elasto-brittle and elastic-partiplasticheskimi (partially plastic) fibers. In the consideration included rheologically unstable state and deformed fibers, which can be realized if the fibers are composed of a stable mechanical system, which in this case the set of fibers in the composite. Posed boundary value problems are solved by special iterative methods. It is shown that, in spite of their global convergence may exist convergence divergence areas and iterations. It was found that the transition from area to area of convergence divergence corresponds to the loss of stability of self-equilibrated stress state in the composite.