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Recent experiments have revealed the strain‐dependent phenomenon of electrical resistance for CNT‐polymer nanocomposites, but at present, no theory seems to exist to explain such observations. In this paper, a strain‐dependent homogenization scheme with considerations of volume change of the nanocomposite and strain‐dependent electron tunneling is developed to this end. The effective electrical conductivity and secant moduli of the nanocomposite are selected as the two homogenization parameters. The thermodynamic driving force and the corresponding evolution equation of the progressive degradation process of the interface are also derived. It is demonstrated that the predicted resistance change ratio and strain sensitivity factor of CNT‐polymer nanocomposites are in close agreement with the experimental results over a wide range of strain loading. With the addition of CNT nanofillers, both theory and experiments show a decrease of resistance change ratio and strain sensitivity factor. As the strain loading increases, the resistance change ratio first increases slightly and then increases rapidly. Among other novel features of the theory, it is also shown that CNT‐polymer nanocomposites can attain a very high strain sensitivity factor even at a low CNT loading. It is believed that this research can provide a practical guidance to the design of high‐sensitivity strain sensors.