This study considers the optical modulation parameters of THz radiation generated via optical-pump terahertz probe spectroscopy, passing through thin films of single-walled carbon nanotubes (SWCNT), attached onto the stretchable substrate. We investigated the dependence of photoconductivity of the stretched film on the elongation and orientation of its direction towards THz beam polarization. We interpreted the changes observed, establishing the key factors affecting the photoconductive pathways. The obtained modulators were characterized practically: the wide range of modulation depths (MD) (up to 100%) and fast lifetimes of photoinduced charge carriers (5 ps) were marked. This research guides the way to construct the devices of switchable optoelectronics, which are of a perspective in the THz data transfer systems.