The thermal stability and irradiation stability of the Mo/Si multilayer in the high temperature and strong radiation environment of the lunar surface are analyzed. The Mo/Si multilayers are measured by hard X-ray diffractometer (XRD) and laser plasma reflectometer (LPR) before and after heating (in a vacuum chamber) at 100 ℃ and 200 ℃. The results show that there is almost no change in the reflectivity and central wavelength of the Mo/Si multilayer. The distribution of the defects and its density in the Mo/Si multilayer is simulated by Mote Carlo method. It shows that the protons and the defects concentrate in the inner of the multilayer with higher energy protons. The Mo/Si multilayers are irradiated by protons with the energy of 60 keV and the dose 3×1012 cm-2 and 3×1014 cm-2 respectively. The erosion defects and nodule defects are observed in the multilayer after irradiation by protons. The results show that the influence on the Mo/Si multilayers is proportional to the dose of the protons with the same energy.