Unidirectional (UD) composites are building blocks in most load bearing structural components for lightweight applications in aerospace, automotive and wind energy industries. The loss of the structural load bearing capacity is governed by the instability of the fiber breakage process in the UD composites. When subjected to increasing or repeated tensile loading along fiber direction, the first failure event within these composites occurs as discrete fibers break at weak points followed by fiber/matrix debonding due to high stress concentration caused by fiber breaks. Upon further loading, or on repeated loading, more fiber breaks occur along with other accumulated damage events such as debond growth and matrix cracking. Final failure of a UD composite occurs when a critical fracture plane is formed by interconnecting individual broken fibers and associated debonding through matrix cracking. This failure process has emerged from numerous experimental studies, which also suggest that the critical fracture plane contains only a small number of broken fibers for commonly used composites such as glass/epoxy and carbon/epoxy. However, the mechanisms underlying the critical fracture plane formation are not clear. As the first step to clarify the creation of a critical fracture plane, the conditions for connectivity of a broken fiber end with neighboring broken fibers is studied in this work. In order to investigate the local stress field surrounding the broken fiber, a finite element (FE) model is constructed in which six neighboring fibers are placed as a ring of concentric axisymmetric cylinder embedded in the matrix. The discrete fiber region is surrounded by a concentric outer cylinder ring of homogenized composite. The entire FE model is subjected to axial tensile loading. To account for the consequence of the stress enhancement at the broken fiber end, a debond crack at the fiber/matrix interface extending a short distance from the fiber end is included in the analysis. Realizing that the debond crack by itself would not connect with other fiber failures, focus of the stress and failure analysis is placed on deviation of the debond crack laterally into the matrix. For this purpose, matrix cracking in two possible modes ductile and brittle is considered, Energy based criteria are used to study the competition between the cracking modes and the crack path into the matrix from the end of debond to the neighboring fibers is determined. Next the failure of the neighboring fibers caused by the intense stress field accompanying the matrix cracks is studied. The conditions for generating a plane connecting the initially broken fiber end to subsequent fiber failures are finally determined. Further ongoing studies are aimed at clarifying the limiting conditions for avoiding the fiber failure criticality, and thereby improving the load bearing capacity of UD composites. The statistical considerations regarding fiber failure will also be incorporated in these studies.