We formulate optical flow estimation as a two-stage regression problem. Based on characteristics of these two regression models and conclusions on modern regression methods, we choose a least trimmed squares followed by a weighted least squares estimator to solve the optical flow constraint (OFC); and at places where this one-stage robust method fails due to poor derivative quality, we use a least trimmed squares estimator to make the facet model fitting robust. This two-stage robust scheme produces significantly higher accuracy than non-robust algorithms and those only using robust methods at the OFC stage. On the synthetic data, the one-stage robust method has an average error of 7.7% against 24% of Black's and 19% of the pure LS method; and the two-stage robust method further reduces the error by half near motion boundaries. Advantages are also demonstrated on real data.