A core structure of a heat exchanger includes seat plates arranged opposite to each other with a predetermined space interposed between them and formed with tube holes, reinforcements connecting the seat plates at their end portions, tubes fixed at its both end portions by insertion into the tube holes, corrugated fins arranged between the tubes, and an upper and lower tanks attached to the seat plates. The tanks are connected by the tubes so that coolant flows between the tanks through the tubes. Tubes arranged at outermost positions of a core part among the tubes are inserted at its end portions by insert members so that the insert members can increase rigidity of the end positions of the outermost positioned tubes and ensure flowing of the coolant between the tanks through the outermost positioned tubes.