Abstract: A transducer stack (10) includes rings (16) of piezo-electric ceramic alternating with metal electrodes (18) along a threaded central shaft (32) extending from a titanium back plate (20). A spacer or threaded element (14) threaded on to the shaft (32) holds the ceramic rings (16) and electrodes (18) in compression against the back plate (20). The transducer stack (10) is mountable eccentrically to a horn (12) of an ultrasonically-vibratable tool, away from an axis of an elongate waveguide (56) extending from the horn (12). The transducer stack (10) may vibrate in a flexural mode perpendicular to the waveguide (56), generating torsional mode ultrasonic vibrations in the horn (12) and waveguide (56), or in a flexural mode parallel to the waveguide (56), generating longitudinal mode ultrasonic vibrations in the horn (12) and waveguide (56).