Stability index distribution of high power solid laser facility requires that the rotation of all the optical elements in the facility can not exceed 0.46 μrad when excited by environmental random vibrations. According to the requirement of stability, back inference the nature frequency design requirement of switchyard mirror frame by pseudo excitation method and random vibration theory, which is one of the large-scale mirror frame. Back inference result is that the nature frequency of switchyard mirror frame can not smaller than 14.88 Hz. Builds the 3-D model and analyses the mode of switchyard mirror frame, the result has a good agreement with the design calculation. Using the PSD as the excitation which had been measured for 24 hours on the install base level of the mirror frame to analyze random vibration response of the mirror frame by the PSD module of ANSYS, the response result is 0.2 μrad. The result indicates that designed mirror frame can meet the requirement of stability index and also indicate that according to the back inference result design the mirror frame is feasibility at the same time.