Release of neurotransmitters from nerve terminals occurs by fusion of synaptic vesicles with the plasma membrane, and this process is highly regulated. Although major molecular components that control docking and fusion of vesicles to the synaptic membrane have been identified, the detailed mechanics of this process is not yet understood. We have developed a mathematical model that predicts how adhesion forces imposed by docking and fusion molecular machinery would affect the fusion process. We have computed the membrane stress that is produced by adhesion-driven vesicle bending and find that it is compressive. Further, our computations of the membrane curvature predict that strong adhesion can create a metastable state with a partially opened pore that would correspond to the 'kiss and run' release mode. Our model predicts that the larger the vesicle size, the more likely the metastable state with a transiently opened pore. These results contribute to understanding the mechanics of the fusion process, including possible clamping of the fusion by increasing molecular adhesion, and a balance between 'kiss and run' and full collapse fusion modes.