In military, Electro-optic/Infra-red system that is used to obtain the target image of high performance induced blur images by the vibration of the carrier and inner optical devices. Optical devices of the EO/IR is constituted by the optical lens, detector and mechanical assembly. High performance detectors for IR camera are typically used for stirling cryocooler to maintain the temperature of the detection surface cryogenically. However, This cooler induces a blur image on detector surface by the vibration. In this study, we performed modal analysis and response analysis of the mounting structure design which can minimize the vibration of the cooler and detector. Also, We confirmed that we were designed robust mounting structure according to the vibration through the response analysis models the inner gimbal and optics.