Currently, biometric methods of personality are becoming more and more relevant recognition technology. The advantage of biometric identification systems, in comparison with traditional approaches, lies in the fact that not an external object belonging to a person is identified, but the person himself. The most widespread technology of personal identification by fingerprints, which is based on the uniqueness for each person of the pattern of papillary patterns. In recent years, many algorithms and models have appeared to improve the accuracy of the recognition system. The modern algorithms (methods) for the classification of fingerprints are analyzed. Algorithms for the classification of fingerprint images by the types of fingerprints based on the Gabor filter, wavelet - Haar, Daubechies transforms and multilayer neural network are proposed. Numerical and results of the proposed experiments of algorithms are carried out. It is shown that the use of an algorithm based on the combined application of the Gabor filter, a five-level wavelet-Daubechies transform and a multilayer neural network makes it possible to effectively classify fingerprints.