Repeatability of interferometry depends on the stability of metrology frame to a certain extent, according to the requirements of stability, structure of the frame is designed. Aiming at the stability problem of high precision metrology frame caused by random vibration, the finite element model of a metrology frame is established, the power spectral density (PSD) measured on the fixed platform is used as the excitation, and then the random vibration response of the frame is analyzed with the PSD module of ANSYS. The analyzed result of stability is 0.5144 nm, and the experimental value is 0.653 nm, they are in good agreement, and the structure of frame and the actual vibration condition meet the stability requirements of metrology frame.