The primary component of the amyloid plaques in Alzheimer's disease (AD) is a highly ordered fibril composed of the 39-43 amino acid peptide, beta-amyloid (A beta). The presence of this fibril has been correlated with both the onset and severity of the disease. Using a combination of synthetic model peptides, solid-state NMR, electron microscopy, and small angle neutron scattering (SANS), methods that allowed fibrils to be studied directly both in solution and in the solid state, the three-dimensional structure of fibrils formed from A beta((10-35)) is assigned. The structure consists of six laminated beta-sheets propagating and twisting along the fibril axis. Each peptide strand is oriented perpendicular to the helical axis in a parallel P-sheet, with each like amino acid residue in register along the sheet. The six sheets are laminated, probably also in parallel arrays, to give a fibril with dimensions of about 60 x 80 Angstrom. Both the methodology developed and the structural insight gained here lay the foundation for strategies to characterize and design materials capable of amyloidlike self-assembly.