The stretching and breaking processes of stilbene-based molecular junctions, which contain S or N atoms in the terminal groups, are studied by using density functional theory. The numerical results show that for pyramid-shaped gold electrodes, a stretching force of about 0.59 nN is needed to break the molecular junction with —S terminals, which is larger than the force of 0.25 nN that is required by the molecule to stretch —SH terminals away from pyramid-shaped gold electrode. However, it is obviously smaller than the force of about 1.5 nN that is needed by the molecule to break —S terminals from planar-shaped gold electrode. If the terminal group is —NH₂ or —NO₂, the force for breaking the molecular junction is about 0.45 nN or 0.33 nN, respectively. More delocalized molecular orbitals formed by the coupling between the frontier occupied orbitals of molecule and electrodes, higher stretching force for breaking molecular junction is required. The natural bond orbital (NBO) analysis shows that more NBO net charges that the terminal atom possesses can enhance the stability of the molecule-electrode contact if there is no bonding orbital formed between end group of molecule and electrode. Based on the numerical results and the combination with previous studies, it can be found that —S terminal and —NH₂ terminal show evident properties in distinguishing tip structures of gold electrodes, which provides useful information for precisely controlling the interactions and interface structures between molecule and electrodes.