Theoretical methods are used to develop models for the ion channel structure of the membrane-bound amyloid beta-protein. This follows recent observations that the beta-protein forms cation-selective channels in lipid bilayers in vitro. Amyloid beta-protein is the main component of the extracellular plaques in the brain that are characteristic of Alzheimer's disease. Based on the amino acid sequence and the unique environment of the membrane, the secondary structure of the 40-residue beta-protein is predicted to form a beta-hairpin followed by a helix-turn-helix motif. The channel structures were-designed as aggregates of peptide subunits in identical conformations. Three types of models were developed that are distinguished by whether the pore is formed by the beta-hairpins, the middle helices, or by the more hydrophobic C-terminal helices. The latter two types can be converted back and forth by a simple conformational change, which would explain the variable conduction states observed for a single channel. It is also demonstrated how lipid headgroups could be incorporated into the pore lining, and thus affect the ion selectivity. The atomic-scale detail of the models make them useful for designing experiments to determine the real structure of the channel, and thus further the understanding of peptide channels in general. In addition, if beta-protein-induced channel activity is found to be the cause of cell death in Alzheimer's disease, then the models may be helpful in designing counteracting drugs.