Abstract: The boundary element method (BEM) was usually used to study the acoustic radiation in moving medium. A key issue of this method was how to calculate the weak integrals while the field point approaching the source point. A new integral method was developed to solve this problem. Using this method, the weak integral on the element surface was divided into singular integral and non-singular integral. For the singular part, analytic solution was obtained through rigorous mathematic derivation. As to the non-singular part, the integral was evaluated by numerical quadrature techniques. One of the major advantages of this method was that it could effectively compute the singular integrals with good accuracy.