Ultrasound system and method configured to locally determine a parameter of nonlinear tissue elasticity by monitoring shear wave propagating through the tissue. The shear wave is caused by an acoustic radiation force (ARF) which is applied to the tissue by ultrasound irradiation locally, in a focal region of the ultrasound beam and which is a function of the intensity of ultrasound irradiation, its time rate, and the featured nonlinearity parameter. The irradiation does not involve a quasi-static compression of the tissue, thereby permitting local estimation of nonlinear tissue elasticity and circumventing the need to solve the global inverse problem.
