The paper addresses the issue of optimal expansion and reconstruction of heat supply systems, which includes a set of general and specific problems. Therefore, a comprehensive approach to their solving is required to obtain a technically admissible and economically sound result. Solving the problem suggests search for effective directions in expansion of a system in terms of allocation of new heat sources, their type, output; construction of new heat networks, their schemes and parameters; detection of “bottlenecks” in the system and ways of their elimination (expansion, dismantling, replacement of heat pipeline sections, construction of pumping stations). The authors present a mathematical statement of the problem, its decomposition into separate subproblems and an integrated technique to solve it. Consideration is given to a real problem solved for a real heat supply system. A set of arising problems is presented. The application of developed methodological and computational tools is shown.