Grazing illumination of a target close to a flat interface as well as evanescent wave illumination of a buried target can produce significant vertical acoustic pressure gradients at a target. A prior experiment [Espana et al., J. Acoust. Soc. Am. 126, 2187 (2009)] demonstrated the selective coupling to a mode of a flat‐ended solid horizontal circular cylinder. The cylinder’s axis was positioned so that the vertical pressure gradient was large at the end of the cylinder. The present investigation explores this coupling for wider variety cylinders in which the end of the cylinder was modified to include a flat paddle. Such a paddle resembles a fin‐like appendage. When a flat vertical paddle is subjected to a vertical pressure gradient, the associated torque on the paddle facilitates the excitation of torsional modes of the solid cylinder. The radiation damping is found to increase for larger paddles. Targets modified in this way facilitate the investigation of specific scattering mechanisms. Coupling to this type of mode is suppressed when the cylinder’s axis is at a pressure anti‐node where the pressure gradient vanishes. [Work supported by ONR.]