So as to make the most of an available irradiation test volume of the gas-cooled high-flux test module of the International Fusion Materials Irradiation Facility, the vessel of the test module is supposed to have a rectangular shape, into which specimens can be packed spatially efficiently. There is a large pressure difference of several atmospheric pressures between the inside and the outside of the vessel because gaseous helium flows inside the vessel to control the temperature of the specimens and a low-vacuum condition is kept outside the vessel for safety reasons. This pressure difference is assumed to cause readily the deformation of the vessel wall. Even a slight deformation should be taken seriously because the deformation of the vessel noticeably affects the coolant flow, that is, cooling performance. In this study, we performed elastoplastic finite element analysis for two rectangular vessels of the high-flux test module proposed by FZK and Kyushu University. In addition to the material nonlinearity, by taking into account the geometrical nonlinearity and thermal stress, we could obtain detailed results such as relations between the deformations and the pressure differences.