THE discovery of carbon nanotubes1,2 has stimulated many theoretical studies of their physical properties3-12, and their bulk synthesis13 should soon make possible experimental measurements of these properties14. All studies so far have assumed that the nanotubes have perfect cylindrical symmetry. Here we show that van der Waals forces between adjacent nanotubes can deform them substantially, destroying this cylindrical symmetry. We present transmission electron microscopy images of two adjacent aligned tubes, about 100 Å in diameter, which show flattening of the tubes along the contact region. Calculations on two-layer nested nanotubes indicate that these deformations can be explained on the basis of van der Waals interactions. We predict that these effects should be observable at least for tubes as small as 20 Å in diameter, and suggest that they may have a significant influence on the tubes' physical properties.