An influence of elastic tensile stress on electrical resistivity of carbon fiber has been investigated as a basic research to develop a strain sensor. The initial elastic stress reversibly decreases the electrical resistivity, although the large stress causing irreversible deformation increases the resistivity. In addition, a linear relationship between initial stress and reduced electrical resistivity is obtained in the initial elastic stress zone. As the initial elastic stress probably enhances the periodicity of graphite structure, decreasing in the electrical resistivity with tensile elastic stress is explained.