Traditionally, heat transfer problems are solved in relation to two-flow systems in which heat exchange is carried out between hot and cold coolants. However, along with two-flow systems, there are often multiflow systems in which the number of coolant flows is three or more. In addition, each energy carrier stream may consist of several components, and the installation may include several stages. Thus, the development of universal approaches and methods for modeling, calculation, and optimization of multi-component multiflow multistage energy complexes within the framework of a unified methodology is an urgent scientific and practical task. A methodology of matrix formalization of modeling heat and mass transfer processes is based on methods and approaches of matrix description of heat and mass transfer systems in energy complexes. The approaches and methods of modeling energy power installations are summarized. Within the framework of the matrix description methodology, the rules and approaches to the development of models of heat and mass transfer processes are formulated in relation to multicomponent multiflow multistage energy complexes. The authors have proposed a solution to the inverse problems with and without considering a phase transition in coolants. Analysis of formulated and solved problems within the framework of the proposed methodology allows us to recommend the use of methods and approaches of matrix modeling of equipment to solve direct and inverse problems for multicomponent multiflow multistage energy complexes for various purposes.