Abstract: The coupled fluid-structure vibration equation is established for bodies in tht half-space fluid domain, especially sitting on the infinite plane, based on the BEM theory. Then, the authors calculate natural frequencies, vibration responses and the acoustic radiation for a box, on which the authors discuss the impact of the soft surface and the hard plane. Finally, the authors study several relative factors including the plate thickness, the structure damping and the distance between the body and the infinite plane. The results of this research show that the impact of the soft surface and the hard plane on the structural natural frequencies, vibration responses and the acoustic radiation cannot be ignored.