THE discovery of fullerenes1,2 and carbon nanotubes3,4 has led to the realization that it should be possible to tailor the properties of graphitic sheets if their geometry can be controlled5-7. In exploring these possibilities, we have found that the folding and tearing of graphitic sheets follow well defined patterns which seem to be governed by the formation of sp3-like line defects in the sp2 graphitic network. Our studies with the atomic force microscope and scanning tunnelling microscope reveal that these folds and tears occur preferentially along the symmetry axes of graphite, and that ’ripples’ are observed in the curved portions of the folds. We also see ripples in deformed carbon nanotubes. They lie along the directions for which sp3-like line defects can form most easily to relieve strain. Our ab initio molecular orbital calculations indicate that the ripples stabilize the pi-electronic energy in the bent structures with the total energy balance being determined by the amount of nuclear repulsion. These results provide insight into the geometries that graphitic structures will preferentially accommodate, and the properties that might ensue.