Abstract: The natural boundary reduction,suggested by Feng and Yu^[2,3],is applied to deal with the exterior boundary value problem of 3-D Helmholtz equation.First,it explains how to derive the natural integral equation,namely the exact Dirichlet-to-Neumann condition,of Helmholtz problem in exterior spherical domain by expansion of spherical harmonics.Second,a numerical method for solving the hypersingular integral equation is developed.Third,some numerical examples are given to illustrate this method.

Key words: Helmholtz equation, the natural boundary reduction, numerical method