The basic theory of fast multipole virtual boundary element method (VBEM) is discussed through expanding the fundamental solution, and the algorithm can make the complexities of operation and memory about solution of the equations to be of linear proportion to the freedoms of the problem. Numerical examples are presented to demonstrate the feasibility, accuracy and efficiency of the method. At the same time, the relationships between the order for expansion and the storage capacity, computing time, precision are analyzed, and the influence of boundary points in the leaf to the calculation efficiency is discussed. The corresponding reference value is put forward for the convenience of engineering application.