Based on the HXMT satellite's structure, the finite element model of this satellite is developed, and static analysis, normal modes and frequency responses are investigated. The maximal stress result of every part of the HXMT satellite and the frequencies in 100 Hz are obtained. The results provide data for optimizing design of the HXMT satellite structure and avoiding synchronous vibration occurring. Considering theory analysis and past design experiences, some reasonable suggestions of optimizing the satellite structure are presented.