The boundary element method is used to solve fluid-solid half-space problems with fluid-filled dimples and air bubbles on the solid surface. The problems, formulated in the Fourier (frequency) domain, are described by the fullspace three-dimensional acoustic and elastodynamic boundary integral equations (BIE), with pressure and displacement serving as primary variables. The techniques developed are general and may be with any kind of incident wave, however, plane waves are used in all numerical experiments. The equations governing the acoustic region are first converted mathematically to equations like those of an elastic region. The two regions are coupled and solved for the displacements using the interface conditions. On obtaining the displacements, the tractions, pressures and pressure gradients are computed using the same interface conditions. The numerical results obtained are verified using reciprocity relations and by comparison with solutions available for the halfspace elastodynamic problem