Electrically conductive nanofibers were fabricated from elastic polyurethane (PU) and PU/multiwalled carbon nanotubes (MWCNTs) nanocomposite by electrospinning method. The nanocomposites were electrospun at various MWCNTs loading. Electron microscopy was used to investigate nanofibers morphology and dispersion of MWCNTs in the electrospun nanofibers. The results showed that the presence of the MWCNTs promoted the creation of fibrous structures in comparison with the PU without MWCNTs. On the other hand, increasing the MWCNTs content resulted in a slight increase in the average fiber diameter. TEM micrographs and mechanical properties of the electrospun mats indicated that the homogeneous dispersion of MWCNTs throughout PU matrix is responsible for the considerable enhancement of mechanical properties of the nanofiber mats. Electrical behavior of the conductive mats was also studied, in view of possible sensor applications. Cyclic experiments were conducted to establish whether the electrical properties were reversible, which is an important requirement for sensor materials.