Bio-inspired fibrillar surfaces with reversible adhesion to stiff substrates have been thoroughly investigated over the last decade. In this paper we propose a novel composite fibril consisting of a soft tip layer and stiffer stalk with differently shaped interfaces (flat vs. curved) between them. A tensile stress is applied remotely on the free end of the fibril whose other end adheres to a rigid substrate. The stress distributions and the resulting adhesion of such structures were numerically investigated under plane strain ( 2 D ) and axisymmetric ( 3 D ) conditions. The stress intensities were evaluated for different combinations of layer thickness and Young’s moduli. The adhesion strength values were found to increase for thinner layers and larger modulus ratio; these trends are also reflected in selected experimental results. The results of this paper provide a new strategy for optimizing adhesion strength of fibrillar surfaces.