An improved method for removing sludge and corrosion products from the interior of a heat exchanger vessel, such as a nuclear steam generator, which comprises the steps of generating a series of pressure pulses within a liquid chelate-containing chemical cleaning agent after the agent has been introduced into the interior of the vessel to create shock waves in the liquid for dislodging, dissolving and fluidizing sludge and corrosion products. The liquid chemical cleaning agent is removed from the vessel after only about 10 to 70 percent of what would have been its normal residence time without the pressure pulses. The method further includes the steps of simultaneously recirculating the chemical cleaning agent through a filter assembly during the pressure pulsing operation in order to remove fluidized sludge and corrosion products dislodged by the pressure pulsing, thereby affording them no opportunity to resettle back onto the surfaces of the heat exchanger vessel and interfere with the chemical cleaning of the vessel. The method reduces not only the time required for a particular chemical cleaning agent to effectively clean the vessel, but further reduces the number of times such chemicals need to be introduced into the vessel, which in turn results in the production of less radioactive liquid waste products.