When we use a conductive fabric as a pressure sensor, it is necessary to quantitatively understand its electromechanical property related with the applied pressure. We investigated electromechanical properties of three different conductive fabrics using the electrical impedance spectroscopy (EIS). We found that their electrical impedance spectra depend not only on the electrical properties of the conductive yarns, but also on their weaving structures. When we apply a mechanical tension or compression, there occur structural deformations in the conductive fabrics altering their apparent electrical impedance spectra. For a stretchable conductive fabric, the impedance magnitude increased or decreased under tension or compression, respectively. For an almost non-stretchable conductive fabric, both tension and compression resulted in decreased impedance values since the applied tension failed to elongate the fabric. To measure both tension and compression separately, it is desirable to use a stretchable conductive fabric. For any conductive fabric chosen as a pressure-sensing material, its resistivity under no loading conditions must be carefully chosen since it determines a measurable range of the impedance values subject to different amounts of loadings. We suggest the EIS method to characterize the electromechanical property of a conductive fabric in designing a thin and flexible fabric pressure sensor.