A curved or bendable micro-electro-mechanical transducer (such as the cMUT) is disclosed. The transducer has a plurality of transducer elements built on a substrate. The substrate has a slot below every two neighboring device elements. Each slot is at least at least partially filled with a flexible material to allow bending of the substrate. A bending actuator may be included to facilitate the bending of the substrate. An exemplary bending actuator uses a nonuniformly shrinkable material to bend the substrate. A curved or bendable cMUT of the present invention can be configured to be an intravascular ultrasound (IVUS) device.