An apparatus and method for estimating and imaging mechanical properties of biological tissues. The apparatus includes one or two ultrasound emitting devices (transducers) that first apply an acoustic radiation force to vibrationally displace a sphere embedded in the medium. Alternatively, a biopsy needle may be inserted into the medium and vibrated along its axis to generate shear waves. During and after vibration, ultrasound is again applied to image shear waves in the medium that propogate from the vibrating sphere or needle. By measuring the local wavelength of the shear waves, the shear modulus and viscous coefficient of the medium surrounding the vibrating element are estimated.