The present invention relates to ultrasonic surgical clamping instruments and, more particularly, to a curved clamp arm for use with ultrasonic surgical instruments that have an ultrasonically actuated blade that, in one case, is ultrasonically actuated to have motion in substantially a single plane. The curved clamp arm opens and closes with respect to the blade and also has a plane of curvature that is parallel to the plane of motion of the blade when the clamp arm is in the closed position, and not parallel to the plane of motion of the blade when the clamp arm is in the open position.