Diaphragm compressors are extensively used in the hydrogen refueling stations, and diaphragm durability is one of the most critical challenges. At the end of the discharge process in the diaphragm compressor, the diaphragm undergoes large deflection deformation stress as it clings to the upper surface of the gas cavity. Additionally, the valve hole machined at the center of the gas cavity introduces additional stress on the diaphragm. In this paper, the theoretical calculation method combining the thin-plate large deflection theory and the thin-plate small deflection theory was used to calculate the diaphragm radial stresses. A numerical simulation method was also applied to investigate the effect of radial stress on the diaphragm. The deviation between the results from both methods was within a reasonable range. Furthermore, the effects of the valve hole diameter, diaphragm thickness and the number of diaphragms on the diaphragm’s radial stresses were also investigated by numerical simulation method. The results indicated that the radial stress at the center of the discharge valve hole increases with the valve hole diameter. And the radial stress at discharge valve hole center initially decreases and then increases, reaching the minimum value of 243.90 MPa when the diaphragm thickness is 0.7 mm.