Interfacial stress distribution of bonded quarter planes subjected a concentrated force was re-investigated based on Bogy’s solution . It’s found that the characteristic length of the singularity of interface end (δ), varies with the index of stress singularity at interface end from millimeter to nanometer. This is a unique characteristic of stress singularity at interface end. How the characteristic length of the singularity of interface end (δ) influences the initial de-bonding of the interface end is a new question worth to pay attention. It’s found in the photoelasticity experiments that usually the debonding initiated at the interface end with singularity, but as the index of stress singularity, as well as the characteristic length of singularity of interface end, decrease to some extent, the initial debonding moves to an inner point near the interface end. This phenomenon clearly shows the index of stress singularity has obvious influence on the debonding of interface end.