A novel numerical scheme is presented for solving the problem of two dimensional Stokes flows with free boundaries
whose evolution is driven by surface tension. The formulation is based on a complex variable formulation of Stokes flow
and use of conformal mapping to track the free boundaries. The method is motivated by applications to modelling the
fabrication process for microstructured optical fibres (MOFs), also known as “holey fibres”, and is therefore tailored for
the computation of multiple interacting free boundaries. We give evidence of the efficacy of the method and discuss its
performance.