Optical axis stability is an important index to determine the detection capability of infrared system in the airborne random vibration environment.In the design stage，a continuous zooming infrared system is taken as the research object.Firstly，the moving lens is identified as the optical axis sensitive element.An accurate finite element model is established for the linear motion mechanism of the lens.Through the integrated optical and mechanical analysis method，the optimization design of the optical and mechanical structure of the continuous zooming infrared system is completed.The finite element modeling method of linear motion mechanism of lens and the optimization design process of optical axis stability proposed in this paper have important reference significance for the subsequent design of random vibration optical axis stability of airborne photoelectric imaging system under random vibration.