In this paper, accurate numerical analyses of the stress distributions within the adhesive in scarf joints under elastic assumption using 3D models are developed. An elastic limit model that takes into account the hydrostatic stress and von Mises equivalent stress, permit to define the more stressed parts of the adhesive with respect to the scarf angle. It is shown that high stress concentrations are generated near the edges and the corners of the specimen at the interface between the substrate and the adhesive. The use of ronded substrates does not lead to decrease significantly these stress concentrations. It is shown that cleaning the free edge of the adhesive changes the location of edge effects without completely erasing them. A modification of the geometry, has been proposed. This modification leads to a quasi-homogeneous distribution of the stresses in the thickness of the adhesive with stresses that tend to 0 near the edges.