A numerical study of the influence of adherend stiffness on adhesive bonded joints provided an insight into some of their fundamental properties. The stress yield in the vicinity of singular locations, in stiff and flexible adherend joints, was investigated. Linear elastic finite element analysis was used to compare the different systems. A special gradual refinement technique in the vicinity of stress singularities was used and proved to be very efficient. Parametric finite element analysis allowed for development of closed form expressions for the stress distribution in the vicinity of the singular points The singular stress distribution zone is limited by the adhesive strip thickness. Thus the stress intensity factors are attenuated in comparison with homogeneous bodies. The stress field in the singular region normalized to the developed stress concentration factor, appears to be invariant, and independent of joint configuration. The subsequent invariability leads to a general relationship between the Stress Concentration Factor SCF, unique for adhesively bonded joints.