Abstract: Based on the theory of exact geometric analysis, the real geometric boundaries are considered, the error created by meshing is decreased, and a new boundary integral equation is introduced. The method of Cauchy principle value integrals and Hadamard finite-part integral are used to solve the problem of singular term integrals. Besides, non-unique solution caused by fictitious frequency is circumvented through the Burton-Miller method. Numerical examples show that the method considering the exact geometric boundary has a good accuracy.