Shear wave elasticity imaging (SWEI) is a new approach to imaging and characterizing tissue structures based on the use of shear acoustic waves remotely induced by the radiation force of a focused ultrasonic beam. SWEI provides the physician with a virtual "finger" to probe the elasticity of the internal regions of the body. In SWEI, compared to other approaches in elasticity imaging, the induced strain in the tissue can be highly localized, because the remotely induced shear waves are attenuated fully within a very limited area of tissue in the vicinity of the focal point of a focused ultrasound beam. SWEI may add a new quality to conventional ultrasonic imaging or magnetic resonance imaging. Adding shear elasticity data ("palpation information") by superimposing color-coded elasticity data over ultrasonic or magnetic resonance images may enable better differentiation of tissues and further enhance diagnosis. This article presents a physical and mathematical basis of SWEI with some experimental results of pilot studies proving feasibility of this new ultrasonic technology. A theoretical model of shear oscillations in soft biological tissue remotely induced by the radiation force of focused ultrasound is described. Experimental studies based on optical and magnetic resonance imaging detection of these shear waves are presented. Recorded spatial and temporal profiles of propagating shear waves fully confirm the results of mathematical modeling. Finally, the safety of the SWEI method is discussed, and it is shown that typical ultrasonic exposure of SWEI is significantly below the threshold of damaging effects of focused ultrasound.