The article substantiates the use of the resistance-acoustic method in problems of non-destructive testing of mechanical stresses or defects in structures of metals and alloys in natural and technical systems. The possibilities of the use of the proposed method for the potential monitored facilities were analyzed, to which the strict requirements for operational security are imposed (bearing reinforced concrete structures, bridges, radio and television towers, etc.). The main approaches to the development of the application methodology of the resistance-acoustic effect in solving the problems of technological control of mechanical stresses and defects in structures of metals and alloys are determined. The mathematical modeling was performed, using basic mathematical models of facilities of the resistance-acoustic control, considering the mutual influence of the elastic and electric fields in electrically conductive media, taking into consideration the parameters of technical state and wear.