The aim of the article is to present the research methodology for determining the bottleneck in a metallurgical company. At the beginning, the importance of simulation methods in production engineering is discussed. Then, the production process of brass rods in a selected company in the metallurgical industry is characterized, taking into account the specificity of individual workstations in real production conditions. It was arbitrarily assumed that statistical models based on a triangular, normal and uniform distribution are used to describe the phenomena occurring in the analyzed production process, adequate to the actual operating conditions at individual production stations. Next, an attempt is made to present the mutual relations between the existing production stations and to combine them into one production system. This was done using the ARENA simulation model. In the proposed approach, the computer simulation allowed us to isolate the bottleneck in the presented technological process of producing brass bars. The theoretical solution was verified using statistical methods in industrial conditions, and the results show the possibility of increasing production efficiency. The conducted research identified the activities and estimated their impact on the occurrence of the bottleneck in the production process.