We describe the MaxFlux algorithm for the computation of likely pathways for global macromolecular conformational transitions. The algorithm assumes an overdamped diffusive dynamics for the biomolecule, appropriate to large scale conformational changes. As an application of the MaxFlux method, we explore conformational transitions between alpha-helical, collapsed coil, and beta-sheet conformations of an amyloid Abeta-peptide. The resulting transition pathways are analyzed in terms of the mechanism of conformational transition and the progression of the peptide energetics in both an aqueous and a membrane-mimicking nonpolar solvent.