A method and apparatus for removing from the tube sheet and transfer tubes of a nuclear steam generator sludge deposits which occur from the use of all volatile treatment water chemistry. A continuously activated suction apparatus maintains at a low level the water/sludge inventory on the tube sheet. A high pressure first water lance is oscillated and stepped inwardly along the central tube lane of the generator to dislodge the sludge from the tube plate and heat exchange tubes. After this lance has been stepped inwardly to a predetermined position, a low pressure second water lance is activated and periodically advanced to a position just short of the first lance and functions both to dislodge sludge and to form a water barrier which prevents redeposition of sludge in the clean area. The flows from both lances combine to produce a high flow of water-suspended sludge which flows across the top of the tube sheet to the annulus of the steam generator where it is removed by the suction apparatus without any redeposition. Suction dams are placed in the vicinity of the suction apparatus in order to increase the efficiency of the removal of the water-entrained sludge by suction.