We reveal that the axial stiffness of amyloid fibrils is inversely correlated with their cross-sectional area. Because amyloid fibrils' stiffness is determined by hydrogen bond (H-bond) density with a linear correlation, our finding implies that amyloid fibrils with larger radial sizes are generally softer and have lower density H-bond networks. In silico calculations show that the stiffness-size relationship of amyloid fibrils is, indeed, driven by the packing densities of residues and H-bonds. Our results suggest that polypeptide chains which form amyloid fibrils with narrow cross sections can optimize packing densities in the fibrillar core structure, in contrast to those forming wide amyloid fibrils. Consequently, the density of residues and H-bonds that contribute to mechanical stability is higher in amyloid fibrils with narrow cross sections. This size dependence of nanomechanics appears to be a global property of amyloid fibrils, just like the well-known cross-beta sheet topology.