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Static and dynamic mechanical deflections were electrically induced in cantilevered, multiwalled carbon nanotubes in a transmission electron microscope. The nanotubes were resonantly excited at the fundamental frequency and higher harmonics as revealed by their deflected contours, which correspond closely to those determined for cantilevered elastic beams. The elastic bending modulus as a function of diameter was found to decrease sharply (from about 1 to 0.1 terapascals) with increasing diameter (from 8 to 40 nanometers), which indicates a crossover from a uniform elastic mode to an elastic mode that involves wavelike distortions in the nanotube. The quality factors of the resonances are on the order of 500. The methods developed here have been applied to a nanobalance for nanoscopic particles and also to a Kelvin probe based on nanotubes.