A comparison of two models of the behavior of the material of a thin adhesive layer and their influence on the value of the J-integral for a specific experimental sample with specified mechanical and geometric properties is considered. A linearly elastic model of behavior and a model that takes into account the zone of weakened bonds with a finite linear distribution of the stress field are studied. The value of the J-integral is determined via the product of the specific work of the stresses and the thickness of the adhesive layer in the area of adhesive bond breaking. It is assumed that the thickness of the adhesive is finite and small compared to the thickness of the cantilever of the DCB sample. The finiteness of the layer thickness makes it possible to determine its deformations at relatively small thicknesses and to find the corresponding energy product. The distribution of stresses in the model with a zone of weakened bonds, determined by the ultimate strength and ductility of the adhesive, introduces the determining value of the J-integral. For an adhesive with pronounced plastic properties, the result of calculating the J-integral, taking into account the finiteness of the stress state, gives a result close to the experiment in comparison with the elastic model.