A closed-form analytical model is developed in this paper to study the perturbed stress field in a general unidirectional composite system containing fiber fractures. The model includes analysis of eccentrically oriented fibers and multiple fiber fractures with the use of an approximating geometry. The theory developed incorporates a functional dependence of stress/strain concentration on constituent material properties, fiber volume fraction, crack size, multiple fiber fracture, and fiber eccentricity. Utilizing a mechanics of materials approach with classic elasticity concepts, the approximate stress field is generated for each constituent region (e.g. fiber, matrix, and interphase). The analysis employs an annular ring of fibers to model the adjacent unbroken fibers and a novel fiber discount methodology to examine multiple fiber fractures. Analytical results of strain concentration are compared with direct experimental measurements to corroborate the model's depiction of the effect specific physical parameters (crack size and axial position) have on this quantity. Parametric studies are performed with variables such as fiber volume fraction, constituent stiffness properties, crack size, and eccentrically located fibers to investigate their significance on general trends.