The present paper deals with the modeling of bonded interfaces adopting the asymptotic expansion technique. The equilibrium problem of a composite body made of two adherents issn perfect contact with an elastic interface is considered and a classical rescaling technique is introduced. The asymptotic expansion method is reviewed; in fact, the representation form for the displacement and stress vector fields are introduced and tsshe effect of higher order terms is taken into account. Using the classical scheme of matched asymptotic expansions, the interface conditions are obtained. The cases of hard and soft interfaces are considered: the first is derived assuming the elasticity coefficients independent of the adherent thickness, the second considers the elasticity properties linearly depending on the thickness. Numerical investigations are performed in the framework of the finite element method. In particular, comparisons of the results obtained by modeling the adhesive as a continuum material (discretized in finite elements even in the thickness) with the results carried out using hard, soft interface models at the first and higher order expansion are performed.