An object of the present invention is to provide a gas turbine combustor with improved fatigue resistance of a combustor. It is possible to intentionally reduce a stiffness of each of flanges of upper and lower walls of an end portion (outlet) of the tail pipe of the gas turbine combustor. It is possible to reduce a stiff difference between the upper and lower walls of the end portion (outlet) of the tail pipe section and side walls. Thus, it is possible to reduce compulsion deformation caused due to thermal stress generated in the end portion (outlet) of the tail pipe section on the operation of the conventional gas turbine combustor, and to reduce high stress easy to generate in the side plate. As a result, the gas turbine combustor with high fatigue resistance can be realized.