Abstract: A theoretical model to describe the acoustic characteristics of plane ultrasonic acoustic waves imping on an acoustic metasurface was developed. The proposed model takes into account the high-order diffracted modes and therefore incorporates mutual coupling among neighboring cavities. With this model, the cavity geometry parameters were optimized to achieve the minimum reflection coefficient and impedance, respectively. Results reveal that the phase opposition between incident and reflective waves at the surface could largely depress the increment ratio of Mack second mode. The proposed effective impedance boundary could open up new possibilities of metasurfaces for hypersonic boundary-layer transition control.