In this paper, we propose a method for the robust and efficient computation of multi-frame optical flow in an expressive sequence of facial images. We formulate a novel energy minimisation problem for establishing dense correspondences between a neutral template and every frame of a sequence. We exploit the highly correlated nature of human expressions by representing dense facial motion using a deformation basis. Furthermore, we exploit the even higher correlation between deformations in a given input sequence by imposing a low-rank prior on the coefficients of the deformation basis, yielding temporally consistent optical flow. Our proposed model-based formulation, in conjunction with the inverse compositional strategy and low-rank matrix optimisation that we adopt, leads to a highly efficient algorithm for calculating facial flow. As experimental evaluation, we show quantitative experiments on a challenging novel benchmark of face sequences, with dense ground truth optical flow provided by motion capture data. We also provide qualitative results on a real sequence displaying fast motion and occlusions. Extensive quantitative and qualitative comparisons demonstrate that the proposed method outperforms state-of-the-art optical flow and dense non-rigid registration techniques, whilst running an order of magnitude faster.