Genetic programming (GP) has been shown to be a powerful tool for automatic modeling and program induction. It is often used to solve difficult symbolic regression tasks, with many examples in real-world domains. However, the robustness of GP-based approaches has not been substantially studied. In particular, the present work deals with the issue of outliers, data in the training set that represent severe errors in the measuring process. In general, a datum is considered an outlier when it sharply deviates from the true behavior of the system of interest. GP practitioners know that such data points usually bias the search and produce inaccurate models. Therefore, this work presents a hybrid methodology based on the RAndom SAmpling Consensus (RANSAC) algorithm and GP, which we call RANSAC-GP. RANSAC is an approach to deal with outliers in parameter estimation problems, widely used in computer vision and related fields. On the other hand, this work presents the first application of RANSAC to symbolic regression with GP, with impressive results. The proposed algorithm is able to deal with extreme amounts of contamination in the training set, evolving highly accurate models even when the amount of outliers reaches 90%.