With the aid of the properties of the hypersingular kernels, a geometric conversion approach was presented in this paper.The conversion leads to a general approach for the accurate and reliable numerical evaluation of the hypersingular surface boundary in-tegrals encountered in a variety of applications with boundary element method. Based on the conversion, the hypersingularity in theboundary integrals could be lowered by one order, resulting in the simplification of the computer code. Moreover, an integral trans-formation was introduced to damp out the nearly singular behavior of the kernels by the distance function defined in the local polar co-ordinate system for the nearly hypersingular case. The approach is simple to use, which can be inserted readily to computer code, thusgetting rid of the dull routine deduction of formulae before the numerical implementations, as the expressions of these kernels are ingeneral complicated. The numerical examples were given in three-dimensional elasticity, verifying the effectiveness of the proposedapproach, which makes it possible to observe numerically the behavior of the boundary integral values with hypersingular kernelsacross the boundary.
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