Apparatus and methods for generating resonantly amplified ultrasound shear waves in biological tissue. The apparatus comprises a plurality of transducer elements and a controller for controlling the element excitation such as to cyclically generate the pattern of focal regions having associates shear waves and to create resonant amplification of the shear waves. Resonant amplification of the shear waves is obtained when shear waves generated at one focal region are superposed in phase on shear waves synchronously generated at an adjacent focal region. The generation may be done by burst or continuous wave excitation. In some embodiments, the shear waves are supersonic shear waves.