A method for dislodging and dislocating scale, sludge, corrosion and other deposits from heat transfer equipment surfaces, such as boiler and heat exchanger surfaces in steam generation systems, which are in contact with aqueous systems. This invention relates to the introduction of an aqueous chemical cleaning solution into the heat exchanger vessel. The aqueous chemical cleaning solution contains a non-corrosive carrier agent and/or a non-corrosive intercalation agent. The carrier agent has the ability to penetrate the matrix of the sludge, scale and other deposits, and the intercalation agent causes the sludge, scale and other deposits to fracture and break apart. This invention relates to generating a series of pressure pulses within the non-corrosive aqueous chemical cleaning solution to create shock waves for dislodging, dissolving and fluidizing sludge and corrosion products. This invention relates to the soaking of scale, sludge and other deposits in aqueous chemical cleaning solutions to dislodge and dislocate the sludge, scale and other deposits. This invention further relates to an operation utilizing a high velocity jet of water, the water containing a chemical cleaning additive, to dislodge and dislocate scale, sludge, corrosion and other deposits from the interior surfaces of heat exchanger vessels, in particular, the interior of the secondary side of nuclear steam generators. The aqueous chemical cleaning solution utilized in the aforementioned soaking operation and the chemical cleaning additive contained in the aforementioned jet of water, may be a chelate agent or a non-corrosive chemical cleaning agent containing a carrier and/or intercalation agent. The non-corrosive chemical cleaning agent may be a lower alkyl amine, e.g., dimethylamine, lower hydroxyalkyl amine, e.g., ethanolamine and pentanolamine, or cyclic dimines, e.g., 1,10-phenanthroline, 2,9-dimethyl-1,10-phenanthroline, 2,2'-bipyrindine and 4,4'-bypyridine, or combinations thereof.