Abstract: In a heat exchanger or similar apparatus using a tube bundle, the tubes are located within a jacket and are connected into a tube sheet. An annular reinforcing member secures the tube sheet to the jacket laterally enclosing the tube bundle. The reinforcing member consists of an inner part and an outer part which can be a unitary member or separate parts welded together. The outer part forms a continuation of the jacket and has a greater thickness than the jacket. The inner part extends radially outwardly from the circumferential periphery of the tube sheet to the outer part and has a frusto-conical shape extending outwardly from at least one of the face surfaces of the tube sheet transversely of its radial direction.