An apparatus, operable with a source of cleaning fluid under pressure, for cleaning external surfaces of heat exchange tubes of an air cooled heat exchanger which tubes are situated in generally horizontal rows vertically separated from each other, thus defining a generally horizontal zone between each two adjacent rows, including a. a spray mat having: i. top and bottom fluid impermeable sheets sealed at their mutual peripheral edges defining at least one chamber with a fluid inlet into said chamber for receiving a flow of the cleaning fluid under pressure, and ii. a plurality of laterally spaced apertures and coupled spray nozzles in the top and bottom sheets which are in fluid communication with the chamber, and b. a positioning mechanism for moving the spray mat transversely into and out of one of the zones between two adjacent rows of the heat exchange tubes.