The executed investigations have shown that it is possible to prepare sheet-like material for laser cutting economically viable and with small amount of power expenditure while using reverse jet cleaning for surface treatment. As compared to conventional jet cleaning technologies efficiency of the reverse jet cleaning is attributed to significant pressure increase (by 25–50 %) when the jet is interacting with the treated surface. The paper proposes a mathematical model on the basis of approximate energy method (upper-bound method) and the model is used for calculation of fracture pressure due to action of the reverse jet on the treated surface which consists of a corrosion deposit layer. A variational problem was solved within a framework of the developed model and the problem solution has made it possible to obtain a theoretical dependence for calculation of minimum fracture pressure value pmin in the point reverse jet impact with a barrier oretical dependence and it has taken into account yielding point of the deformed material ss, density of fractured material med material r, jet velocity uстр and parameter of reverse flowing – jet reduction ratio l. Comparison theoretical data and experimental ones (experimental data have been obtained while using a differential pressure transducer ЭДП-30 and a spring dynamometer with measuring limits 25 and 80 MPa, respectively) has shown difference by 4–15 %. Determined insignificant difference between a theory and an experiment demonstrates that the obtained theoretical dependence is considered as a quite correct one and it can be used in engineering practice for prediction of power and kinematics parameters which are necessary for selection of the required pump equipment designed for realization of reverse-jet cleaning process.