The single fiber fragmentation test is commonly used to determine interfacial shear strength. However, the results of the test are still considered suspect by some researchers. To elucidate the issues in the single fiber fragmentation, the test technique, reduction analysis and research achievements in the theoretical and experimental studies are briefly summarized. In this paper, the stress singularity near the interface end is investigated to evaluate the reliability of the fragmentation test. According to the local failure modes near the interface end of a fiber fragment, there are three cases of the interface end conditions to be considered for the fragmentation tests: (A) fiber breaks only, without matrix cracking and de-bonding, (B) fiber breaks and matrix cracks, without interface de-bonding, (C) fiber breaks and interface de-bonds, with or without matrix cracking. After the singularity analysis of the stress field near the interface end was determined, it became apparent that the interfacial shear strength given by the fragmentation test is not entirely valid because a stress singularity exists near the interface end.