Automated ultrasonic scanning of a chestwardly compressed breast of a supine patient uses a scanning assembly that moves down to compress the breast through a membrane that is secured to the assembly across a bottom opening. A motorized ultrasound transducer moves across the breast while the breast remains downwardly compressed against the patient's chest, sending and receiving ultrasound energy through the membrane. The membrane is porous with respect to an acoustic coupling liquid that impregnates it. The transducer outputs ultrasound information that is processed to form initial planar images and then reconstructed slice images of breast tissue.