A bypass duct portion is provided in a casing of an EGR cooler so that heat distortion is absorbed, and the EGR cooler body and a valve case are brazed / fixed together so as to improve strength of the valve case, whereby, the bypass duct portion is formed between an inner surface of the casing and the core, a switch is provided for switching and guiding the exhaust gas to either of the core or the bypass duct portion, and a number of outer ribs formed in the circumferential direction respectively are arranged side by side while being separated from each other in the longitudinal direction in the bypass duct portion of the casing to form a heat stress absorbing portion. Also provided is a cylindrical valve case that is integrally formed by deep drawing of a thin metal plate by a press machine, a pair of slits are provided at the rear end of the valve case, both edges of an intra-valve partition plate are inserted into the slits, support projection portions are provided on both faces of the both edge portions of the intra-valve partition plate, and the edge of the slit is supported by the support projection portion. An opening of the valve case is integrally brazed / fixed to an opening of a header portion of the casing.