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Active sites and ligand-binding cavities in native proteins are often formed by curved β sheets, and the ability to control β-sheet curvature would allow design of binding proteins with cavities customized to specific ligands. Toward this end, we investigated the mechanisms controlling β-sheet curvature by studying the geometry of β sheets in naturally occurring protein structures and folding simulations. The principles emerging from this analysis were used to design, de novo, a series of proteins with curved β sheets topped with α helices. Nuclear magnetic resonance and crystal structures of the designs closely match the computational models, showing that β-sheet curvature can be controlled with atomic-level accuracy. Our approach enables the design of proteins with cavities and provides a route to custom design ligand-binding and catalytic sites.