This thesis reports our research on developing a new method to image the electric conductivity and relative permittivity of biological tissues. The first method is Differential Frequency Magneto-Acousto-Electrical Tomography (DF-MAET) to image the electrical impedance of biological tissues with high spatial resolution. It is shown that DF-MAET signal is caused by the vibrations of the sample at a difference frequency (DF) because of the radiation force. In the second method, we investigated the possibility of using a novel mechanism for imaging the electrical permittivity of biological tissues. Theoretical study shows that a magnetic moment will be produced in biological tissues when both and ultrasound wave and an electrical field exist in the tissue. We report the results to detect this magnetic moment with both coils and electrodes attached to the tissue. We were able to detect the signal with electrodes, but its frequency dependence indicates that this signal is due to the impedance modulation by ultrasound, and that it is not related to the relative permittivity. Finally, we studied the ultrasonic vibration potentials generated in fat and muscle tissues.