Ultra-stable optical cavities are widely used for laser frequency stabilization. In these experiments the laser performance relies on the length stability of the Fabry-Perot cavities. Vibration-induced deformation is one of the dominant factors that affect the stability of ultra-stable optical cavities. We have quantitatively analysed the elastic deformation of Fabry-Perot cavities with various shapes and mounting configurations. Our numerical result facilitates a novel approach for the design of ultra-stable cavities that are insensitive to vibrational perturbations. This approach can be applied to many experiments such as laser frequency stabilization, high-precision laser spectroscopy, and optical frequency standards.