The device (30) has a calculating unit (37) for calculating the intrinsic displacement of medium from a set of ultrasonic lines (L1-L3) forming an acquisition (3a). A processing unit (36) is provided for processing the ultrasonic lines (L1, L2) with the help of relative parameter (3b) before or during the formation of an ultrasonic line (L3) of an acquisition (3a) to determine the intrinsic displacement (3d-L1) of biological tissues from the ultrasonic lines (L1, L2). An independent claim is also included for a method for measuring viscoelastic properties of biological tissues by processing of ultrasonic waves reflected by the biological tissues.