Poly(styrene-beta-isobutylene-beta-styrene)-poly(3-hexylthiophene) (SIBS-P3HT) conducting composite fibers are successfully produced using a continuous flow approach. Composite fibers are stiffer than SIBS fibers and able to withstand strains of up 975% before breaking. These composite fibers exhibit interesting reversible mechanical and electrical characteristics, which are applied to demonstrate their strain gauging capabilities. This will facilitate their potential applications in strain sensing or elastic electrodes. Here, the fabrication and characterization of highly stretchable electrically conducting SIBS-P3HT fibers using a solvent/non-solvent wet-spinning technique is reported. This fabrication method combines the processability of conducting SIBS-P3HT blends with wet-spinning, resulting in fibers that could be easily spun up to several meters long. The resulting composite fiber materials exhibit an increased stiffness (higher Young's modulus) but lower ductility compared to SIBS fibers. The fibers' reversible mechanical and electrical characteristics are applied to demonstrate their strain gauging capabilities.