Despite a large number of diverse methods and approaches to studying the enterprise stability, forecasting of stable development in the Ukrainian economy did not yield sufficiently precise results. Therefore, the main purpose of the study was to develop a complex of economic and mathematical models for estimating and analyzing the enterprise functioning stability in the dynamics, which will allow timely diagnosis of its instability and taking effective management decisions. The proposed complex of models is based on the logistic approach and the classical apparatus of the systems automatic control theory. The structural model of the enterprise was developed, which resulted in its generalized transfer function in the market environment. The generalized transfer function is the basis of the construction of a simulation model for assessing the enterprise functioning stability. This approach allowed the use of algorithmic mathematical methods – the criteria of Hurwitz and Mikhailov to study the stability of the enterprise functioning in the dynamics. According to the performance indicators of the two enterprises, practically applying the models developed in the work, the research and analysis of the stability of their functioning were carried out. As a result, the appearance of the Mikhailov’s hodograph for a stable and unstable system is clearly demonstrated, and the stability margin is determined. It is important that the obtained models and results, with the appropriate adaptation, can be extrapolated to study the stability of the production and sales enterprise functioning in different economic sectors of different countries of the world. The prospect of further research is seen in the development of an information and analytical system that uses the models for assessing and analyzing the enterprise functioning stability and allows you to change the structural model quickly, adjusting it to certain features of a particular enterprise. This will allow you to determine the level of stability for any investigated system operatively.