For terahertz wave applications, tunable and rapid modulation is highly required. When studied by means of optical pump–terahertz probe spectroscopy, single-walled carbon nanotube (SWCNT) thin films demonstrated ultrafast carrier recombination lifetimes with a high relative change in the signal under optical excitation, making them promising candidates for high-speed modulators. Here, combination of SWCNT thin films and stretchable substrates facilitated studies of the SWCNT mechanical properties under strain and enabled the development of a new type of an optomechanical modulator. By applying a certain strain to the SWCNT films, the effective sheet conductance and therefore modulation depth can be fine-tuned to optimize the designed modulator. Modulators exhibited a photoconductivity change of approximately 2 times of magnitude under the strain because of the structural modification in the SWCNT network. Stretching was used to control the terahertz signal with a modulation depth of around 100% without strain and 65% at a high strain operation of 40%. The sensitivity of modulators to beam polarization is also shown, which might also come in handy for the design of a stretchable polarizer. Our results give a fundamental grounding for the design of high-sensitivity stretchable devices based on SWCNT films.