Double lap adhesively bonded joints were found to present a difficulty in interpreting experimental results in the neighborhood of each extremity of the overlap. The adhesive-air boundary cannot sustain a shear stress, but it is generally impossible to take account of this condition with the order of magnitude of our assumptions on the stress-distribution through the thickness of the specimen. An experimental analysis with electrical strain-gages suggests a new approach based on the matched asymptotic expansions method. Two configurations are chosen, the moderately thin joint and the very thin joint, with respect to the mechanical characteristics of each component of the specimen. In the case of the moderately thin joint, a comparison between theoretical and experimental results is given.