The permeability stress sensitivity of the ultra-low permeability sandstone rock is experimentally studied in this paper. Unlike the 1D rock plug sample in the classical method, the 2D flat sandstone rock sample is used in this experiment and the synthetic formation water is used as the fluid medium. In addition, the permeability stress sensitivity of the 2D rock sample is compared with that of the conventional 1D rock plug sample. A novel research method for determining the rock permeability stress sensitivity is proposed. The experimental results indicate that the type of the fluid media and the size of the rock sample have a significant influence on the permeability stress sensitivity. The permeability stress sensitivity of the 2D flat rock sample is shown to be weaker than that of the conventional 1D rock plug sample. The relationship between the permeability and the effective stress of the 2D sample is close to that of the 1D plug sample when the brine is used as the fluid media. But it is different from that of the 1D plug sample when the nitrogen is used as the fluid media. The permeability stress sensitivity of the 2D sample is almost similar to that of the 1D plug sample in the lower effective stress range. However, the former is weaker than the latter in the higher effective stress range because the effective stress in the 2D sample is not uniform. The local permeability stress sensitivity at different sites is different from each other in the 2D sample. The effective stress has a more significant influence on the permeability in the main flow lines and the near production well regions.