Here we report a non-toxic β-type titanium alloy exhibiting unstable elastic and plastic deformation behavior. Elastic instability leads to remarkable elastic softening, i.e., the decrease of incipient Young’s modulus with slight pre-straining. In spite of partial recovery during room-temperature aging, a stable modulus of 33GPa matching that of human bone can be maintained. Plastic instability causes highly-localized deformation which is very effective in grain refinement but contributes little to strength. We thus obtain soft nanostructured metallic materials (NMMs): The flow stress increases by only ∼5.5% as coarse grains are reduced to below 50nm, in contrast with several times increase for previously-reported NMMs.