In this study, nanofibers obtained through the electrospinning process are explored for strain-sensing applications. Thermoplastic polyurethane (TPU) flexible structures were fabricated using the solution electrospinning process (SEP) technique. Subsequently, these structures were nanomodified with single-walled carbon nanotubes (SWCNTs) through immersion into an ultrasonicated suspension containing 0.3 wt% SWCNTs. The nanomodification aimed to impart an electrically conductive network to the structures. Micro-tensile tests and electrical resistance measurements were conducted to characterize the apparent mechanical and electrical properties, respectively. The fabricated structures demonstrated potential as wearable strain sensors for monitoring changes in strain across various applications. The samples exhibited excellent performance, high sensitivity, outstanding mechanical properties, and a broad stretching range. Scanning electron microscopy (SEM) observations provided qualitative insights into the activated conductive pathways during operation.