A multipolar expansion technique is applied to the indirect formulation of the boundary element method in order to solve the two-dimensional internal Stokes flow second kind boundary value problems. The algorithm is based on a multipolar expansion for the far field and numerical evaluation for the near field. Due to the nature of the algorithm, it is necessary to resort to the use of an iterative solver for the resulting algebraic linear system of equations. A parallel implementation is designed to take advantage of the natural domain decomposition of fast multipolar techniques and bring further improvements. Copyright © 2000 John Wiley & Sons, Ltd.