abstract:Dual boundary integral equations for elasticity problems with a smooth boundary are derived by using the contour approach surrounding the singularity. Both two and three-dimensional cases are considered. The potentials resulted from the four kernel functions in the dual formulation have different properities across the smooth boundary. The Hadamard principal value or the so called Hadamard finite part, is derived naturally and logically and is composed of two parts, the Cauchy principal value and the unbounded boundary term. After collecting the free terms, Cauchy principal value and unbounded terms, the dual boundary integral equations of the problems are obtained without infinity terms. A comparison between scalar (Laplace equation) and vector (Navier equation) potentials is also made.