Simulations using the Finite Element Method (FEM) play an increasingly important role in the design process of joints and fasteners in the aerospace industry. In order to utilize the potential of using adhesive bonding, there is an increasing need for effective and accurate computational methods. The geometry and the nature of an adhesive joint is, however, not so simple to describe effectively using regular FEM-codes. The main reason is that the very thin and soft adhesive layer must be modelled by a large number of FEM-elements in the thickness direction to achieve sufficiently accurate calculations. To overcome this difficulty, special FEM-elements can be developed that provides a material surface treatment of the adhesive and the joined parts. In order to create a model that reflects the above features one may introduce proper scalings on the geometry and on the material properties in terms of a perturbation parameter. Within the framework of three-dimensional elasticity, together with an asymptotic expansion method, a material surface model is obtained through a systematic procedure of derivation. In such derivation no a priori assumptions on the displacements or stress fields are needed. The final result is a variational equation posed over a single reference surface, which forms the basis of a structural element for the compound joint.