A simple model is proposed which predicts the hardness of a coated substrate as a function of coating thickness and indentation depth. The model is based on an analytical solution for the stress and strain fields around a pressurized coated spherical cavity, taking into account elastic and perfectly plastic deformation. The predictions of the coated cavity model can be applied to the plane coated surface by making various geometrical correspondences, and the model shows good agreement with finite-element calculations and experimental results for the case of a hard film on a soft substrate. For the less important case of a soft film on a harder substrate the cavity model is less successful for the plane coated surface geometry, owing to bulging at the free surface.