To study the dynamic performance of an integrated rectangular mirror used for THz ultra high speed imaging, a random vibration response analysis is conducted on its structure. This paper elaborates on the random vibration response analysis method based on random basic excitation, and designs a finite element model of an integrated rectangular rotating mirror using the finite element simulation analysis software ANSYS. And compared the results of modal module simulation analysis with real measurements, it is found that the difference between simulation calculation and actual data is less than 4%, which verifies the correctness and accuracy of the established model. For the vibration response of an integrated rectangular-like rotating mirror under axial and radial random excitations, finite element random vibration response calculations are performed. By comparing the random vibration experiments under axial excitation with the simulated analysis results, the probability that the rotating mirror is subjected to a stress exceeding 37.029 MPa is only 0.3%, which is far lower than the yield limit strength of the material. The study identifies some issues in the current design and summarized preliminary improvement plans through analysis, and provides important reference for future research and development of rotating mirrors.