We consider coupled structures consisting of two different linear elastic materials bonded along an interface. The material discontinuities combined with geometrical peculiarities of the outer boundary lead to unbounded stresses. The mathematical analysis of the singular behaviour of the elastic fields, especially near points where the interface meets the outer boundary, can be performed by means of asymptotic expansions with respect to the distance from the geometrical and structural singularities. The coefficients in the asymptotics, which are called generalized stress intensity factors, play an important role in classical fracture criteria. In this paper we present several formulas for the generalized stress intensity factors for 2D and 3D coupled elastic structures. The formulas have the form of scalar products or convolution integrals of the given data or the unknown displacement field and the so–called weight functions, similar to Maz'ya/Plamenevsky functionals introduced in [19] for elliptic boundary value problems. The weight functions are non–energetic elastic fields, which admit a decomposition into a known singular part and a more regular one, which is computed by boundary element domain decomposition methods. Numerical experiments for two–dimensional problems illustrate the theoretical results.