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－ As a further development of the authors′ work (Huang and Qian, 1993), in this paper a newnumerical method based on the time domain boundary element technique is proposed for solving fluid-sol-id coupling problems, in which a rigid body impacts normally on the calm surface of a half-space fluid. Afundamental solution to the half-space potential flow problem is first derived with the method of images.Then, an equivalent boundary integral equation in the Laplace transform domain is established by meansof Green′s second identity. Through the inverse Laplace transform and discretization in both time andboundary of the fluid region, the numerical calculation for the problem under consideration has been car-ried out. Several examples demonstrate that the present method is more efficient than existing ones, fromwhich it is also seen that the shape of the impacting body has a considerable effect on the total impactforce.