Ultra-narrow linewidth frequency-stabilized lasers play a crucial role in the fields of precision measurement, precision spectroscopy, atomic frequency standard and other fields, and its frequency stability depends on the performance of the reference ultra-stable cavity. The horizontally placed ultra-stable cavity is highly sensitive to external vibrations. Usually, there is a magnitude difference between actual vibration sensitivity and its theoretical design, which makes vibration noise an important factor limiting the stability of the ultra-stable cavity. This paper takes a cylindrical horizontal cavity as an example and proposes a cavity design with a low vibration-sensitive of 7.3×10-12/g (g=9.81 m·s^-2) based on the finite element analysis method. Error factors affecting vibration sensitivity during processing and assembly are analyzed, and the corresponding solutions are proposed. It is indicated that the method proposed in this work is also applicable to vibration-insensitive designs of other shapes of ultra-stable cavities, and can be used in various precision measurement experiments in the future.