In the world of information technology, there is often the threat of fraud. One of the well-known tools of fraudsters is voice conversion. This paper models an attack on a text-independent speaker verification system using the following voice conversion methods: Hifi-VC, Diff-VC, DiffHier-VC and Vosk-VC. The research aims to evaluate the effectiveness of these voice conversion methods in spoofing attacks against a modern ResNet-based verification system. The English-language speech corpus TIMIT is used as input data for the voice conversion. It was used to obtain four new datasets, which were used in modeling an attack on the text-independent speaker verification system. The entire experiment is divided into three main phases, which are distinguished by the ratio of original audio recordings to fake ones. The value of Equal Error Rate (EER) was used as the criterion for evaluating effectiveness when testing the text-independent speaker verification system. According to the results of the modeling, it was concluded that the conversion methods used are effective in attacking the text-independent speaker verification system because the EER value increased with the increasing number of fake audio recordings. The DiffHier-VC method was the most efficacious, elevating the EER by 325% and 525% in Stages 2 and 3 of the experiment, respectively. The statistical significance of these results was confirmed by the Wilcoxon signed-rank test. The results of the study can be used in further training of speaker verification systems.