Abstract In this article, we develop a novel indirect second kind integral equation formulation for the solution of the mixed boundary value problem for Stokes flow between two closed surfaces (multiple‐connected domain). At the exterior surface the fluid velocity is specified (boundary condition of the first kind) and at the interior surface the fluid surface traction is given (boundary condition of the second kind). The theoretical background to the proposed technique is explained in detail, including mathematical proofs of existence and uniqueness of solution. Numerical results of test examples are included to validate the formulation. As expected, the numerical solution of the proposed approach is very stable under iterative solvers requiring few numbers of iteration to achieve a desirable accuracy, even for very large number of surface nodes. Copyright © 2001 John Wiley & Sons, Ltd.