Far ultraviolet IMaging Spectrograph (FIMS) should be designed to maintain its structural stability and to minimize optical performance degradation in launch and in operation enviroments. The structural and thermal analyzes of grating and grating mount system, which are directly related to FIMS optical performance, was performed using finite element method. The grating mount was made to keep the grating stress down, while keeping the natural frequency of the grating mount higher than 100 Hz. Transient and static thermal analyzes were also performed and the results shows that the thermal stress on the grating can be attenuated sufficiently. The optical performance variation due to temperature variation was with the allowed range.