Measuring the performance of railway undertakings is inevitably becoming a prerequisite for their survival on the market in today's dynamic and highly turbulent environment. Railway undertakings must find optimal solutions in order to efficiently and effectively operate, survive on the transport market, and develop and maintain their competitive advantages as well. The objective of this research is to define and evaluate the criteria that affect the efficiency of railway undertakings, increase their competitiveness and propose a DEA-based approach (i.e. a Data-Envelopment-Analysis-based approach) to the assessment of the efficiency of railway undertakings in increasing competitiveness. In order to solve the criteria selection problem, the Fuzzy Analytical Hierarchical Processes (FAHP) method was experimented with, which showed the priority of the assessment of the efficiency of railway undertakings, on the basis of the five groups of criteria. The criteria in a group that outperformed the other criteria in that group for their freight transport railway undertakings within a composite normalized range were used as the input and output indicators for the DEA. The evaluation of the efficiency of the railway undertakings was considered by using the DEA approach. The results show that the proposed approach successfully enables the consolidation of a set of criteria (resource, operational, financial, quality and safety) into a single assessment of the efficiency of the railway undertakings, while providing information on the corrective actions that can improve the efficiency of the railway undertakings.