Aggregation of Amyloid beta (A beta) peptide has been linked to the neurodegenerative Alzheimer's Disease and implicated in other amyloid diseases including cerebral amyloid angiopathy. A beta peptide is generated by cleavage of the amyloid precursor protein (APP) by transmembrane proteases. It is crucial to determine the structures of beta-amyloid peptides in a membrane to provide a molecular basis for the cleavage mechanism. We report the structures of amyloid beta peptide (A beta(1-40) and A beta(1-42)) as well as the 672-726 fragment of APP (referred to as A beta(1-55)) in a membrane environment determined by replica-exchange molecular dynamics simulation. A beta(1-40) is found to have two helical domains A (13-22) and B(30-35) and a type I beta-turn at 23-27. The peptide is localized at the interface between membrane and: solvent. Substantial fluctuations in domain A are observed. The dominant simulated tertiary structure of A beta(1-40) is observed to be similar to the simulated A beta(1-42) structure. However, there are differences observed in the overall conformational ensemble, as characterized by the two-dimensional free energy surfaces. The fragment of APP (A beta(1-55)) is observed to have a long transmembrane helix. The position of the transmembrane region and ensemble of membrane structures are elucidated. The conformational transition between the transmembrane A beta(1-55) structure, prior to cleavage, and the A beta(1-40) structure, following cleavage, is proposed.