The problem of development of mathematical models and computer programs for calculation and forecast of various long-wave processes occurring in the reaches of reservoirs and hydro-systems is considered. The basic method to solve the problem is a mathematical modeling based on differential equations for the channel flow – the Saint-Venant equations using numerical methods. Conventional methods in hydraulics, methods for building mathematical models based on the laws of hydromechanics and their numerical calculations are also used. A mathematical and a computer program to carry out forecast calculations of long-wave processes occurring in the reaches of hydro-systems and reservoirs have been developed. The reliability of the results obtained is confirmed by rigorous mathematical statement, the use of well-known and tested equations and methods of hydraulics, and by the agreement of the results obtained in the work with the data obtained by other authors and available in literature.