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In order to enhance the strength of single-lap joints, the single-lap joints with reinforcements were proposed. The influence of reinforcement length on the singular behavior near to the interface point of single-lap joints was investigated theoretically and numerically. The theoretical strength of singularity point was calculated by Bogy determinant. Stresses along the interface close to the singularity points were calculated with finite element analyses (FEAs). Results showed that the singular stress intensity factor of single-lap joints can be decreased by the reinforcement. However, the singular stress intensity factor of single-lap joints with reinforcements was decreased slightly with increasing reinforcement length.