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The elastic properties of soft tissues are closely related to their structure, biological conditions, and pathology. For years, physicians have used palpation as a crude elasticity measurement tool to diagnose diseases in the human body. Based on this simple concept, but using modern technology, several elasticity imaging schemes have been developed during the past two decades. In this paper, we present two elasticity imaging methods that use a low-frequency (Hz to kHz range) harmonic force to excite the tissue. The first method, called magnetic resonance elastography (MRE), uses a phase sensitive magnetic resonance technique to detect tissue motion. Excitation is usually performed with a mechanical actuator on the surface of the body, although other excitation methods are possible. In the second method, called vibro-acoustography, the radiation force from focused ultrasound is used for excitation in a limited region within the tissue. Tissue motion is detected by measuring the acoustic field emitted by the object in response to the vibration. The resulting images in both methods can be related to the dynamics of the object at the excitation frequency. The spatial resolution of MRE and vibro-acoustography images is in the millimeter and sub-millimeter ranges, respectively. Here, we present the theory and physical principles of MRE and vibro-acoustography and describe their performances. We also present results of experiments on various human tissues, including breast, brain, and vessels. Finally, we discuss potential clinical application of these two imaging methods.