The presence of a sill alters the traditional flat seabed conditions, imposing significant effects on hydrodynamic characteristics of the wave–body interaction problem. Eigenfunction matching method (EMM), which is a typical analytical method, is employed to precisely evaluate these effects on two-dimensional radiation of linear water waves by a rectangular buoy. The agreement with the published data and numerical results by the boundary element method (BEM) indicates the correctness of the present EMM. Four aspects involving varying height of the sill, varying width of the sill, varying water depth of the right semi-infinite subdomain, and varying relative positions between the buoy and the sill are considered. Analytical results show that among all the hydrodynamic coefficients, the added mass coefficient of heave is affected most by the varying sill.