We study the aggregation of peptides using the discrete molecular dynamics simulations. Specifically, at temperatures above the alpha-helix melting temperature of a single peptide, the model peptides aggregate into a multilayer parallel beta-sheet structure. This structure has an interstrand distance of 4.8 A and an intersheet distance of 10 A, which agree with experimental observations. Our model explains these results as follows: hydrogen-bond interactions give rise to the interstrand spacing in beta sheets, while Gō interactions between side chains make beta strands parallel to each other and allow beta sheets to pack into layers. An important feature of our results is that the aggregates contain free edges, which may allow for further aggregation of model peptides to form elongated fibrils.