The mechanical stability, a key problem for the 3rd synchrotron light source, is essential for the electron beam performance. This paper analyzes the influences of the first eigenfrequency and Q value on the mechanical stability. Then the research on the improvement of the mechanical stability for the magnet girder assemblies (MGAs) and the dipole concrete assemblies (DCAs), both of which are the main parts of the Shanghai Synchrotron Radiation Faculty (SSRF), is performed. The measurement result shows that the mechanical stability is improved obviously for the MGAs by using the auxiliary supports and for the DCAs by using polymer-modification concrete instead of common concrete. The paper can give some guidance to the mechanical design of the 3rd generation light sources.