The fiber breakage behavior of unidirectional polyacrylonitrile (PAN)-based carbon fiber/epoxy composite material was estimated, taking into account stress concentration in the adjacent fibers resulting from matrix cracking around fiber breakages. Analysis of the breakage behavior of adjacent fibers in double-fiber fragmentation tests showed that the results of simulation conducted using a spring element model and taking into account the stress concentration on the fiber surface corresponded well with experimental results. In addition to considering the stress concentration, it is essential to employ a bimodal Weibull distribution, which is a narrow strength distribution in the high strength-region, to explain the behavior observed in double-fiber fragmentation tests. When carbon fiber with no treatment and no sizing agent was used, matrix cracking around fiber breakages did not occur, and the tensile strength of unidirectional carbon fiber/epoxy composites was improved. These findings suggest that there is considerable potential for improving the tensile strength of composites by suppressing stress concentration on the fiber surface.