Amyloid fibrils characterized as highly intractable thread-like species are associated with many neurodegenerative diseases. Although neither the mechanism of amyloid formation nor the origin of amyloid toxicity is currently completely understood, the detailed three-dimensional atomic structures of the yeast protein Sup35 and Abeta amyloid protein determined by recent experiments provide the first and important step towards the comprehension of the pathogenesis and aggregation mechanisms of amyloid diseases. By analyzing these two amyloid peptides which have available crystal structures and other amyloid sequences with proposed structures using computational simulations, we delineate three common features in amyloid organizations and amyloid structures. These could contribute to an improved understanding of the molecular mechanism of amyloid formation, the nature of the aggregation driving forces that stabilize these structures and the development of potential therapeutic agents against amyloid diseases.