We use elastomeric polydimethylsiloxane substrates to strain single-walled carbon nanotubes and modulate their electronic properties, with the aim of developing flexible materials that can sense local strain. We demonstrate micron-scale nanotube devices that can be cycled repeatedly through strains as high as 20% while providing reproducible local strain transduction by via the device resistance. We also compress individual nanotubes, and find they undergo an undulatory distortion with a characteristic spatial period of 100-200 nm. The observed period can be understood by the mechanical properties of nanotubes and the substrate in conjunction with continuum elasticity theory. These could potentially be used to create superlattices within individual nanotubes, enabling novel devices and applications.