A heat exchanger has a plurality of fluid flow tubes secured adjacent their ends by tube sheets. Cleaning elements are adapted to shuttle back and forth in the tubes and are adapted to be captured by baskets. A basket retaining plate is fixedly mounted, as by bolts or the like, in spaced relationship outwardly from the outer tube sheet face. The plate and its mount cooperate with the tube sheet to hold the baskets in fixed position relative to the tube sheet and tube ends. The outer capturing and holding portions of the baskets extend outwardly from the retaining plate. The baskets include central or intermediate portions which extend through openings in the plate and inner portions which extend through the space between the plate and tube sheet and which terminate within the tube sheet openings. The baskets are fixedly secured against transverse shifting by a two-point support, one at the inner basket ends and one intermediate their ends. To hold the baskets in longitudinally fixed position, and in one embodiment, the basket intermediate portions are threaded to the retaining plate. In another embodiment, shoulders adjacent the inner basket ends engage the plate and tube sheet. The retaining plate is of lesser diameter than the tube sheet and is provided with unobstructed fluid flow openings between the baskets and basket-receiving openings.