A study of the mechanical behaviour of a composite film-substrate material during the hardness test is undertaken. An analytical calculation is proposed applying the kinematic model to the case of the coated spherical cavity problem. The aim of this paper is to discuss the parameters that influence the mechanical behaviour, in order to understand the observed experimental results. The parameters studied are the size of the plastic deformed region, the ratio between the yield stresses of the film and the substrate and the relative work-hardening ratios of both materials. The results show that an important parameter that influences the composite behaviour is the size of the plastic deformed region. The other parameters play an important role in the definition of the size of this region and influence the hardness behaviour as well in a direct way.