The mechanical cues that adherent cells derive from the extracellular matrix (ECM) can effect dramatic changes in cell migration, proliferation, differentiation, and apoptosis. Model ECMs composed of collagen fibrils formed from purified collagen are an important experimental system to study cell responses to mechanical properties of the ECM. Using a self-assembled model system of a film composed of 100-200 nm diameter collagen fibrils overlaying a bed of smaller fibrils, we have previously demonstrated changes in cellular response to systematically controlled changes in mechanical properties of the collagen. In this study, we describe an experimental and modeling approach to calculate the elastic modulus of individual collagen fibrils, and thereby the effective stiffness of the entire collagen thin film matrix, from atomic force microscopy force spectroscopy data. These results demonstrate an approach to the analysis of fundamental properties of thin, heterogeneous, and organic films and add further insights into the mechanical and topographical properties of collagen fibrils that are relevant to cell responses to the ECM.