This paper presents a novel minutiae matching method that deals with elastic distortions by normalizing the shape of the test fingerprint with respect to the template. The method first determines possible matching minutiae pairs by means of comparing local neighborhoods of the minutiae. Next a thin-plate spline model is used to describe the non-linear distortions between the two sets of possible pairs. One of the fingerprints is deformed and registered according to the estimated model, and then the number of matching minutiae is counted. This method is able to deal with all possible non-linear distortions while using very tight bounding boxes. For deformed fingerprints, the algorithm gives considerably higher matching scores compared to rigid matching algorithms, while only taking 100 ms on a 1 GHz P-III machine.