Human amylin is a 37 amino acid residue peptide hormone whose fibrillogenesis has been correlated with type 2 diabetes. These fibrils are rope-like bundles of several 5nm diameter protofilaments. Here, we propose, as a model for the protofilament, a variant of the parallel superpleated beta-structure previously derived for amyloid filaments of the yeast prion Ure2p. In the amylin model, individual polypeptides from residues 9 to 37 have a planar S-shaped fold with three beta-strands. These serpentines are stacked in register, with a 0.47 nm axial rise and a small rotational twist per step, generating an array of three parallel beta-sheets in cross-beta conformation. The interior, the two "bays" sandwiched between adjacent sheets, are occupied by non-polar and by polar/uncharged residues that are predicted to form H-bonded ladders, similar to those found in beta-helical proteins. The N-terminal peptide containing a disulfide bond occupies an extraneous peripheral position in the protofilament. The left-handed twist of the beta-sheets is shown to underlie left-handed coiling of amylin protofilaments in fibrils. The model is consistent with current biophysical, biochemical and genetic data and, in particular, affords a plausible explanation for why rodent amylin does not form fibrils.