Abstract: A tube bundle heat exchanger with baffles is disclosed wherein a tube bundle is housed within an inner casing which is acted upon from both the inside and the outside by a heating medium. The inner casing is not stressed by pressure caused by the heating medium since the medium flows both within and without the casing. The part of the circumference of each baffle which is in contact with the inner casing is tightly connected to the inner casing in order to prevent leak flows. Adjacent heat exchanger tubes of the tube bundle are separated from one another by a zigzag-shaped dividing wall. The dividing wall forms space-economical rerouting channels with the baffles. The tubes of the tube bundle are located parallel to the longitudinal axis of the heat exchanger, and therefore longitudinal in the longitudinal rerouting channels. The heating medium which flows through the rerouting channels flows across the tubes producing favorable heat transfer conditions.