There is presented the practical application example of the theory of constraints, in the paper. In all enterprises from engineering industry, the main problem connected with realization of production orders are the constraint existing in every production system. Searching and increasing of the bottleneck (constraint) should be the first step in situation, when exist necessity to increase production. There are described principles and stages of the production system improvement, which are based on the mentioned above theory. In the paper, there is demonstrated that the Computer simulation is very useful aiding tool for finding constraints and facilitating the analysis of different proposed changes in production systems.