The bonding positions of three isostatic mounts on the primary mirror of a Cassegrain telescope under self-weight loading have both been studied in the paper. Finite element method and Zernike polynomial fitting are complementarily applied to the ZERODUR® primary mirror with a pre-designed lightweight configuration on the back. Eight bonding positions of isostatic mounts with respect to the center of gravity of the mirror have been chosen to investigate the mirror surface deforms as well as the induced optical aberrations. It is found that astigmatism becomes remarkably higher than other optical aberrations under self-weight loading. The optimum bonding position with the least astigmatism value has also been obtained.