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The vibration environment of an inertial navigation system（ INS） can bring an adverse effect on its measurement accuracy. A random vibration model of an optical fiber INS is proposed. It is used by a substructure synthesis method based on frequency response functions. According to this model,a design sensitivity expression in terms of partial derivatives of shock absorber physical parameters and root mean square（ RMS） response of IMU is presented. Compared with the central difference method,the analytical method is verified via a numerical example. Besides,the stiffness of the shock absorber is optimized in order to minimize the rotation of IMU. The result demonstrates that the rotation of IMU is obviously reduced,and the system’s vibration coupling is effectively suppressed by the proposed method. It shows that the method is effective.