<p>Recently, Rim et al. (Rim et al (2023) Eng. Anal. Boundary Elem. 151:19–29) studied wave scattering and radiation by a fully submerged structure separately. This paper is concerned with a oscillating motion of an arbitrarily shaped floating structure near a wall such as vertical breakwater by considering wave diffraction and radiation simultaneously. The structure floating on horizontally semi-infinite water domain is transferred into two structures floating on water domain unlimited in horizontal directions by use of image method. A virtual circular cylindrical surface is chosen as an artificial interface in order to separate the entire water region into an exterior water subregion with infinite volume and an interior water subregion with infinite volume. An exact Dirichlet-to-Neumann (DtN) map on the virtual interface is analytically obtained from a solution for the exterior problem, and it is utilized in the numerical calculation of the two floating structures in the interior water subregion by use of boundary integral equation. Upon comparison with antecedent analytical results for a floating cylinder, the model is escalated to consider the effects of distance from the wall, heading angle, and draft on oscillating motion of a floating chamfer box. The present approach can be adopted to predict the motion responses and wave forces of an arbitrarily shaped floating body in front of a vertical breakwater under a linear incident wave.</p>