Currently, a specific mathematical apparatus and methods of mathematical modeling are used to evaluate and verify translations. The theory is just developing and in this article we will show the application of modeling methods on a specific example of studying toponyms.The article is devoted to the consideration of the problem of using toponyms with the connotation inherent in biblicalism in translations of poetic works of the Ukrainian writer I. Franko. A comparative analysis of Russian and English translations clearly shows the discrepancies in the choice of translation strategies that were used in relation to these onyms by Russian and English translators. An attempt to evaluate the quantitative aspect of the comparative analysis of the work of I. Franko in the translation by D. Brodsky, V. Azarov, V. Rich, V. Semenin, P. Dyatlov, P. Kandy and B. Melnik was identified as a research task. © 2020 The Authors, published by EDP Sciences.