We demonstrate that the tip of an atomic force microscope (AFM) can be used to control the shape and position of individual multiwalled carbon nanotubes dispersed on a surface. Specifically we can bend, straighten, translate. rotate, and-under certain conditions-cut nanotubes. Such manipulations are feasible due to the interaction between nanotubes and the substrate, which can stabilize highly strained nanotube configurations. Direct evidence for this interaction is provided by the study of elastic distortions of tubes interacting with other tubes and the substrate, From the observed deformations of nanotubes with 100 Angstrom diameter. For example, we obtain a binding energy of 0.8 +/- 0.3 eV/Angstrom. This interaction forces nanotubes to conform to the structure of the substrate, and the resulting distortions should induce corresponding changes in their electronic structure and electrical transport properties.