Abstract: In terms of the Fast Multipole Boundary Element Method(FM-BEM), translations with complex function format and main computational steps of the fundamental solution were presented for 2D Stokes flow problem. An algorithm with modified interaction list was obtained and its computational efficiency was analyzed. Truncation errors of the multipole expansion were discussed and a formula for the number of  expansion  terms was given, which showed that the truncation error can be controlled by the number of expansion terms