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In the course of global trends, the development and application of information technologies have emerged as a valuable source of the economy at both the micro and the macro levels. According to the results of the best practice, the application of a piece of software with failures is known to possibly to serious consequences. The analysis and elimination of potential failures in commercial software is the problem that represents one of engineers’ most important tasks. In this paper, a new integrated model for the evaluation and ranking of software failures is proposed. The cost aspect is integrated into the traditional severity index. The assessment of the severity indices, as well as a possibility of detection, is based on the Failure Mode and Effects Analysis - FMEA framework. The weights of the overall severity index, the occurrence of failures, and the possibilities of detection are calculated by applying the best-worst method. The determination of the rank of the identified failures is given by applying conventional Technique for Order of Preference by Similarity to Ideal Solution - TOPSIS. The priority of the activities that are undertaken in order to eliminate the identified failures corresponds to the obtained rank of the failures. The proposed model is illustrated by real-life data.