A tube support device comprises an elongated strip inserted in a tube lane between the tubes of the tube bundle. Raised-tube-engaging zones are disposed in transverse rows across the strip at successive longitudinal locations along its length; these tube-engaging zones extend laterally outwards from both faces of the strip to engage with tubes on opposite sides of the tube lane. The tube-engaging zones may be arranged so that they extend from the two faces of the strip in an alternate manner, with the tube-engaging zones in each row alternately extending from one face and then from the other along the row.