Aluminum ion optical clock transition has a natural linewidth of 8 mHz. The detection laser's linewidth must be ~1 Hz to obtain the optical clock transition spectral line. The semiconductor laser has a linewidth of 500 kHz and a long-term drift of 90 MHz/h. The laser frequency is locked on the Fabry-Pérot (F-P) cavity to meet the requirements of aluminum ion spectral detection. One of the main noises of the F-P cavity is vibration noise. To reduce the vibration sensitivity of the F-P cavity, this study theoretically analyzes the vibration sensitivity of the F-P cavity with stable laser frequency. The finite element method is used to investigate the relationships between the elastic deformation of the F-P cavity as well as its shape and support position. An F-P cavity is designed with a laser vibration sensitivity of 0.53 kHz/(m·s²) at a laser wavelength of 534 nm. It provides a theoretical foundation for realizing low vibration noise lasers and has important applications in the fields of atomic clocks and precise spectrum measurement.