Subject. The article considers structural transition processes in macroeconomics. Objectives. The aim is to present our own concept and mathematical tools to study structural transitions in macroeconomics. Dynamic inter-industry balance enables to formalize the problem in the form of a Koshi task for ordinary differential equations. Methods. The methodology components include the basics of inter-industry and numerical analysis and modeling of linear or linearized dynamic systems, integral criteria of system dynamics, stability and quality of transitional processes. We also apply a technique for analyzing the own dynamic properties of economic systems that solve the same sustainability-related challenges, but on the basis of algebraic methods and criteria. Results. We offer methods and mathematical tools for numerical study of sustainability and structural dynamics of macroeconomics. These methods are focused on integrating high-dimensional balance models and integral criteria for the quality of transition periods in the economy. The paper unveils advantages of calculating the matrix exponential and its integral in tasks involving analysis and forecasting, over other numerical methods. The proposed method permits to effectively build a difference scheme to integrate with any step of observation of the solution. In this case, the work step of integration is generated in the algorithm automatically, depending on changes in gross output. Conclusions. The paper presents a unique option to analyze transitional processes in macroeconomics. It is designed to develop and evaluate the results of pursued economic policy.