A new numerical method, the boundary point method, used for calculating the acoustic radiation problem caused by a vibrating body is presented. The gist of the new numerical method is to replace the coeffcient matrices [A] and [B] in the system equation with the particular solution matrices which are formed of the particular solutions generated by fabricated sources. In the boundary point method, it is unnecessary to consider the interpolating operation and the singular integral which is indispensable for the BEM also does not exist. By avoiding the direct computation for the coeffcient matrices, the boundary point method can improve the calculation speed substantially while maintaining the calculation precision. Another advantage of the method is that it can be used for calculating the acoustic parameters (such as the sound pressure, etc.) at any desired point in the sound field without calculation of the acoustic parameters on the surface. Finally, the boundary point method can overcome the non-uniqueness problem at the characteristic wave numbers effectively. The boundary point method put forward by the authors is applied to the calculation of the exterior acoustic radiation problem caused by a vibrating body. A detailed description of this method is presented. A test for the boundary point method is carried out on the aspects of its calculation precision and speed, adaptation to the geometric shape of vibrating body as well as effectiveness to overcome the non-uniqueness problem through various examples with different shapes and different boundary value distributions. An experiment on the exterior acoustic radiation of a vibrating rectangular box is performed in a semi-anechoic chamber.