An imaging system comprises a device to excite mechanical waves in elastic tissue, a device for measuring the resulting tissue motion at a plurality of locations interior to the tissue at a number of time instances, a computing device to calculate the mechanical properties of tissue from the measurements, and a display to show the properties according to their location. A parameter identification method for calculating the mechanical properties is based on fitting a lumped dynamic parametric model of the tissue dynamics to their measurements. Alternatively, the mechanical properties are calculated from transfer functions computed from measurements at adjacent locations in the tissue. The excitation can be produced by mechanical vibrators, medical needles or structures supporting the patient. The measurements may be performed by a conventional ultrasound imaging system and the resulting properties displayed as semi-transparent overlays on the ultrasound images.