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A sensor was made of a polymer composite composed of electrically-conductive carbon nanotubes embedded in elastic polyurethane. The composite was prepared using a polyurethane filter membrane, enmeshing it, and melding together with carbon nanotubes. Testing has shown that the composite can be elongated as much as 400% during which the electrical resistance is increased 270 times. The composite is also sensitive to compression and to organic solvent vapors. These properties indicate the composite could have applications as a highly-deformable strain and chemical vapors sensing element and also as flexible electromagnetic shielding or protection against lightning. As an example of the use of the composite as a strain sensor, the pressure variation between a shoe and floor during walking and knee flexion during cycling has been monitored.