Abstract:In this paper, we review the free terms of dual boundary integral equations for the Laplace and Navier equations of 2-D and 3-D problems and extend to biharmonic equation for plate problems. We derive the free terms of the dual BIE with a smooth boundary by means of the Taylor series expansion for the density through bump-contour technique surrounding the singularity. After using the limiting approach, the free terms and boundary terms for the 16 improper integrals in the dual formulation for the plate problems are derived. The contributions of single, double, triple and quadrapole potentials for the free term are also examined. The improper integrals due to the 16 kernels with singularity, hypersingularity or super-singularity are interpreted by the Cauchy principal value as well as finite parts.