The following paper presents a simple, inexpensive and scalable method of production of carbon nanotube-polyurethane elastomer composite. The new method enables the formation of fibers with 40% w/w of nanotubes in a polymer. Thanks to the 8 times higher content of nanotubes than previously reported for such composites, over an order of magnitude higher electrical conductivity is also observed. The composite fibers are highly elastic and both their electrical and mechanical properties may be easily controlled by changing the nanotubes content in the composite. It is shown that these composite fibers may be easily integrated with traditional textiles by sewing or ironing. However, taking into account their light-weight, high conductivity, flexibility and easiness of molding it may be expected that their potential applications are not limited to the smart textiles industry.