Cu2+ binding to Alzheimer's β (Aβ) peptides in amyloid fibrils has attracted broad attention, as it was shown that Cu ion concentration elevates in Alzheimer's senile plaque and such association of Aβ with Cu2+ triggers the production of neurotoxic reactive oxygen species (ROS) such as H2O2. However, detailed binding sites and binding structures of Cu2+ to Aβ are still largely unknown for Aβ fibrils or other aggregates of Aβ. In this work, we examined molecular details of Cu2+ binding to amyloid fibrils by detecting paramagnetic signal quenching in 1D and 2D high-resolution 13C solid-state NMR (SSNMR) for full-length 40-residue Aβ(1-40). Selective quenching observed in 13C SSNMR of Cu2+-bound Aβ(1-40) suggested that primary Cu2+ binding sites in Aβ(1-40) fibrils include Nε in His-13 and His-14 and carboxyl groups in Val-40 as well as in Glu sidechains (Glu-3, Glu-11, and/or Glu-22). 13C chemical shift analysis demonstrated no major structural changes upon Cu2+ binding in the hydrophobic core regions (residues 18-25 and 30-36). Although the ROS production via oxidization of Met-35 in the presence of Cu2+ has been long suspected, our SSNMR analysis of 13CεH3-S- in M35 showed little changes after Cu2+ binding, excluding the possibility of Met-35 oxidization by Cu2+ alone. Preliminary molecular dynamics (MD) simulations on Cu2+-Aβ complex in amyloid fibrils confirmed binding sites suggested by the SSNMR results and the stabilities of such bindings. The MD simulations also indicate the coexistence of a variety of Cu2+- binding modes unique in Aβ fibril, which are realized by both intra- and intermolecular contacts and highly concentrated coordination sites due to the in-register parallel β-sheet arrangements.