The single fiber fragmentation test has been continuously used to determine the interfacial shear strength. However, the results of the tests were still suspected by some researchers. To evaluate the reliability of the fragmentation test, the stress singularity near the interface end of fragmentation is investigated. 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 stress field near the interface end was depicted, it is obvious, that the interfacial shear strength given by the fragmentation test is not proper, because of that a stress singularity exists near the interface end.