We report on the mechanical characterization of individual mature amyloid fibrils by atomic force microscopy (AFM) and AFM-based single-molecule force spectroscopy (SMFS). These self-assembling materials, formed from the 29-residue amphiphatic peptide hormone glucagon, were found to display a reversible elastic behaviour. Based on AFM morphology and SMFS studies, we suggest that the observed elasticity is due to a force-induced conformational transition which is reversible due to the beta-helical conformation of protofibrils, allowing a high degree of extension. The elastic properties of such mature fibrils contribute to their high stability, suggesting that the internal hydrophobic interactions of amyloid fibrils are likely to be of fundamental importance in the assembly of amyloid fibrils and therefore for the understanding of the progression of their associated pathogenic disorders. In addition, such biological amyloid fibril structures with highly stable mechanical properties can potentially be used to produce nanofibres (nanowires) that may be suitable for nanotechnological applications.