The constraint effect on the fracture behaviour of a rubber-modified epoxy was investigated using compact tension (CT) adhesive joints. An elastic-plastic finite element analysis was conducted to evaluate the stress distribution ahead of the crack tip in the bulk adhesive and adhesive joints of different bond thickness. The models with sharp and finite radius crack tips were evaluated in the analyses. The constraint effect of adherends on the stress triaxiality ahead of the crack tip in the adhesive joints were discussed. The constraint parameters were investigated using the J-Q theory and the J-CTOD relationship. It was found that as the adhesive thickness was increased, the stress triaxiality ahead of the crack tip was relieved by the remarkable deformation of the adhesive material. Similarly, the crack tip constraint was reduced with increasing bond thickness so that the fracture energy increased towards the value of the bulk adhesive. A higher constraint was associated with a lower fracture energy and vice versa. Furthermore, the J-integral did not have a unique relationship with the crack-tip opening displacement (CTOD) for different adhesive bond thickness, as this depends on the constraint around the crack tip. The results of this study will help improve reliability assessment of adhesive joints in engineering applications.