When sheet of paper is folded along a closed curve, it buckles dramatically. When cut, it collapses and lies flat. We have developed a mechanical model to explain the shape of an elastic sheet folded along a curve that incorporates the geometric frustration inherent in the folded structure. As the curved fold becomes wider, geometrical effects play a more prominent role. The buckled shapes become more rigid to avoid stretching within the sheets on either side of the fold.