We studied natural relative deformations of fingerprints using the methods of elasticity theory [1,2]. As shown by experiments, the registration of deformations results in almost 3 times improvement for direct overlap matching. Principal components of deformations (eigen deformations) are obtained here from the statistics of genuine matches of fingerprints from several public available databases [3,4]. Energy and cross-compatibility analysis for eigen deformations bases carried out on different datasets are adduced in couple with the examples of implementations where dimensionality reduction in the representation of elastic deformations yields significant advantage.