Managing the systems which behaviour is non-deterministic is one of the most important problems in modern management theory. Today, systems with structural and behavioural complexity are prevalent in all areas of human activity, and therefore, their research is of the utmost importance. Such systems, as opposed to deterministic systems, are called non-deterministic. They are characterised by difficult predictable behaviour determined both by external random influences, and within the systems themselves. A clear example of a non-deterministic system is crowds of people, factories, and computer networks and systems. The problem of non-deterministic behaviour directly within the context of professional activities can be seen using an example of building syntactic analysers. The aim of the paper is to design a class of systems oriented towards supporting elements of a discrete event model. The target of research is to simulate discrete event models. The subject of research is a creation of a discrete event model based on the behaviour of an undetermined finite state automaton. During the preparation of the paper, there was developed and practically implemented an algorithm for the application, which materializes the principle of working with threads. The results obtained in the paper are aimed at solving the problem of parallel data processing based on the parallelism of NFA's (non-deterministic finite automaton) behaviour when reading the input string characters. As a result, this should have a positive impact on the regulation of the simulation processes of a non-deterministic system, increasing its efficiency and stability. In conclusion, the algorithm of the application work is disclosed and conclusions about the effectiveness and efficiency of its development are drawn.