The mechanical properties of collagen fibrils play an important role in cell-matrix interactions and are a manifestation of their molecular structure. Using a, to our knowledge, novel combination of uniaxial, longitudinal straining and radial nanoindentation, we found that type I collagen fibrils show a pronounced nonlinear behavior in the form of strain stiffening at strains from 0 to 15%, followed by strain softening at strains from 15 to 25%. At the molecular scale, this surprising phenomenon can be explained by the combination of unfolding of disordered domains and breaking of native cross-links at different stages of strain. Fibrils cross-linked artificially by glutaraldehyde do not show such a behavior, and nanoindentation allowed us to measure the mechanics of the overlap and gap regions in the D-banding individually. The results could have consequences for our understanding of matrix mechanics and the influence of excessive glycation, which has been linked with age-related diseases such as diabetes. Furthermore, the simplicity of the straining method could be attractive in other areas of biophysics at the nanometer scale because it does not require any bespoke instrumentation and is easy to use.