Mutual forces can be induced between coupled structures when illuminated by external acoustic waves. In this Letter, we propose a concept of asymmetric interaction between two coupled plate-like structures, which is generated by oppositely incident plane waves. Besides the striking contrast in magnitude, the mutual force induced by one of the incidences can be tuned extremely strong due to the resonant excitation of the flexural plate modes. The highly asymmetric interaction with enhanced strength in single side should be potentially useful, such as in designing ultrasound instruments and sensors.