Experimental indications that adsorbed lipid vesicles are deformed on the surface (e.g., on SiO(2)) and that the deformation seems to be more pronounced for larger vesicles have been reported. In general, it has been assumed that larger vesicles should show a stronger tendency for spontaneous rupture, which is also backed up by thermodynamic considerations (Seifert, U.; Lipowsky, R. Phys. Rev. A 1990, 42, 4768; Seifert, U. Adv. Phys. 1997, 46, 13). However, using a newly developed model of a lipid bilayer, simulations were performed to study the shape of adsorbed lipid vesicles for different vesicle sizes, with the observation that larger vesicles indeed are more deformed on the surface, but that there is no additional tendency for larger vesicles to rupture spontaneously. It is shown here that the radius of curvature, on the portions of the vesicle membrane that are most strained, is practically independent of the vesicle size. A kinetic barrier for vesicle rupture is proposed to be the reason for the observed disagreement with thermodynamic theory.