In carbon nanotube transistors, typically part of the nanotube is covered by a metal contact. This covered region plays an important role due to the significant electron transfer length. Here we predict that capillary and van der Waals forces cause the nanotube to deform or even collapse under the metal. Nanotubes are known to collapse when their diameters are above some critical value around 4 nm. Under the metal, we find that spontaneous collapse occurs for diameters down to ∼ 1.5-1.6 nm, close to the range used in high-performance transistors. Even at smaller diameters, we find surprisingly large deformations that could significantly affect the electronic structure.