There is provided an EGR cooler having a core portion in which a large number of flat tubes through which exhaust gases pass are stacked one on another in an interior of a hollow cylindrical shell to be joined to the shell for heat exchange between the exhaust gases and a cooling fluid which flows around the tubes, a cylindrical inlet header which is joined to an upstream side of the shell in relation to a gas flow at one end thereof, and a cylindrical outlet header which is joined to a downstream side of the core portion in relation to the gas flow at one end thereof, characterized in that the inlet header and the outlet header are joined to an outer surface of the shell, and the tubes are joined to an inner surface of the shell at those joint portions.