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A key challenge in the design of engineering couplings and contacting components relates to the development of an understanding of the comparative performance of contrasting contact geometries for a given application, including loading, applied deformations and geometrical space envelope. Although fretting is observed in many mechanical assemblies such as keyway-shaft couplings, shrink-fitted couplings, one specific example which has motivated the present work is the pressure armour layer of a marine flexible riser, where the groove and nub experience fretting contact damage. A Hertzian cylinder-on-flat contact geometry is commonly assumed for this groove-nub contact due to the ready availability of the contact (normal and tangential) analytical solutions for this geometry. In reality the contact geometry is closer to a rounded punch-on-flat. The present work adopts a finite element methodology to compare the significance of the Hertzian assumption to that of a rounded punch-on-flat, in terms of fretting behaviour.