Optical axis stability is an important indicator of the detection capability of an infrared optical system. Due to the lack of effective means of evaluation at the design stage, the stability check of the optical axis relied too much on the fitting and adjusting process formerly. Taking an infrared optical system as the object of study, we proposed a method to locate sensitive mirrors and structural modes for the optical axis. Based on LOS equations, the Multi-Point Constraint (MPC) equation between the optical-axis offset and rigid-body displacement of mirror surfaces is constructed. And the offset law of the optical axis changing with the temperature and its response spectrum under the effects of random vibration are obtained. The method presented has great significance for the stability design of the optical axis for complex optical systems.