Nanoscale electronics seeks to decrease the critical dimension of devices in order to improve performance while reducing power consumption. Single-walled carbon nanotubes fit well with this strategy because, in addition to their molecular size, they demonstrate a number of unique electronic, mechanical and electromechanical properties. In particular, theory(1-8) predicts that strain can have a large effect on the band structure of a nanotube, which, in turn, has an influence on its electron transport properties. This has been demonstrated in experiments where axial strain was applied by a scanning probe(9-12). Theory also predicts that torsional strain can influence transport properties, which was observed recently in multiwalled nanotubes(13). Here we present the first experimental evidence of an electromechanical effect from torsional strain in single-walled nanotubes, and also the first measurements of piezoresistive response in a self-contained nanotube-based nanoelectromechanical structure.