A headerless heat exchanger has a core comprised of a stack of flat tubes of rectangular cross section through which a first heat exchange fluid passes. The tubes are expanded in height at their end portions to provide spaces between adjacent plate pairs for passage of a second heat exchange fluid between the tubes. The sides of the tubes are coplanar, at least in the end portions of the tubes, to provide flat surfaces along which the core is sealed to side plates of the heat exchanger, for example by brazing or welding. The side plates may be separately formed or may comprise part of a continuous housing. The tubes are preferably formed from plate pairs having nesting side walls.