Summary: The evaluation of a domain integral is the dominant bottleneck in the numerical solution of viscous flow problems by vorticity methods, which otherwise demonstrate distinct advantages over primitive variable methods. By applying a Barnes-Hut multipole acceleration technique, the operation count for the integration is reduced from \(O(N^2)\) to \(O(N \log N)\), while the memory requirements are reduced from \(O(N^2)\) to \(O(N)\). The algorithmic parameters that arenecessary to achieve such scaling are described. The parallelization of the algorithm is crucial if the method is to be applied to realistic problems. A parallelization procedure which achieves almost perfect scaling is shown. Finally, numerical experiments on a driven cavity benchmark problem are performed. The actual increase in performance and reduction in storage requirements match theoretical predictions well, and the scalability of the procedure is very good.