A recently developed curved interface adhesion test has been analyzed by a 3D-finite-element modelling to calculate the stress distribution along the interface between two different polymer materials. Depending on the material arrangement and the geometry at the wedge of the specimen there may or may not exist stress singularities for elastic behaviour of the components. By using the general analytical solution for the stresses of the wedge problem, the finite-element modelling provides the power of the stress singularity by a regression analysis of the variation of stresses with the distance from the edge. There exist certain values of interface curvature for certain material combinations for which the stress singularity disappears. Consequently, a uniform stress field develops during tensile loading of such bimaterial specimens with a curved interface. With the calculated maximum normal stress concentration that develops at the pole of the interface and the experimental determined critical force for debonding initiation, the adhesion strength can be determined.