A finite element model of a layered hemisphere contacting a rigid flat, which includes the effect of adhesion, is developed. In this analysis elastic-plastic material properties were used for each of the materials comprising the layered hemisphere. The inclusion of the effect of adhesion, which was accomplished with the Lennard-Jones potential, required a special procedure. This configuration is of general theoretical interest in the understanding of adhesion. It has also been suggested as a possible design for a microswitch contact because, with an appropriate choice of metals, it has the potential to achieve low adhesion, low contact resistance, and high durability. The effect of the layer thickness on the adhesive contact was investigated. In particular the influences of layer thickness on the pull-off force, maximum contact radius, and contact resistance were determined. The results are presented as load versus interference and contact radius versus interference for loading and unloading from different values of the maximum interference.