Since the original work of Buckle concerning the substrate influence on the hardness measurement of thin film, more than 20 models were proposed to separate the contribution of the substrate. Subsequently to the development of these numerous models, a question arises: Which is the most relevant models among them? Indeed, the authors usually consider that their proposed model leads to the best prediction of the film hardness which is probably correct for a given experimental condition applied to a particular material. In addition, the authors also assume that the other models are not so relevant. But to have a Sound discussion about the existing models, it is necessary to correctly apply them according to the author statement. In this paper, we better specified the application of the Jonsson and Hogmark model and that of Chicot and Lesage applied to the results obtained on copper films by Beegan et al. Contrarily to these authors, we show that the above-mentioned models lead to a good representation of the experimental data and a good predicted value of the film hardness. (C) 2009 Elsevier B.V. All rights reserved.