The relevance of mathematical modelling lies in finding the correct quantitative characteristics (indicators, parameters) of the effectiveness of the functioning of the process under study, identifying quantitative estimates of the relationships between its elements. Based on the simulation results, the best parameters of the designed equipment and the optimal or rational variant of the production process are selected. The characteristics of the process may vary depending on the purpose. In technological tasks, they are related to the quality of the products and productivity, and the components of any process are usually taken into account simultaneously. The purpose of this study is to analyze various aspects of the use of mathematical modelling in the design of production business processes. In the study course, the mathematical modelling essence was analyzed, the features of the mathematical model development were determined, and the features of mathematical modelling of production business processes were revealed. The author concludes that the mathematical basis for modelling production processes is used at all levels and typologies of business processes starting from micro-processes of task execution or product production to the macro-processes of enterprise management or order (project) implementation. The complexity of using the mathematical base lies in the diversity of business processes and a wide variety of production processes, which requires constant development of numerical methods and algorithms for the correct implementation of the processes themselves and their complex chains.