We present a structural model for amyloid fibrils formed by the 40-residue beta-amyloid peptide associated with Alzheimer's disease (Abeta(1-40)), based on a set of experimental constraints from solid state NMR spectroscopy. The model additionally incorporates the cross-beta structural motif established by x-ray fiber diffraction and satisfies constraints on Abeta(1-40) fibril dimensions and mass-per-length determined from electron microscopy. Approximately the first 10 residues of Abeta(1-40) are structurally disordered in the fibrils. Residues 12-24 and 30-40 adopt beta-strand conformations and form parallel beta-sheets through intermolecular hydrogen bonding. Residues 25-29 contain a bend of the peptide backbone that brings the two beta-sheets in contact through sidechain-sidechain interactions. A single cross-beta unit is then a double-layered beta-sheet structure with a hydrophobic core and one hydrophobic face. The only charged sidechains in the core are those of D23 and K28, which form salt bridges. Fibrils with minimum mass-per-length and diameter consist of two cross-beta units with their hydrophobic faces juxtaposed.