Single lipid vesicles adsorbed on SiO(2) were manipulated using an atomic force microscope (AFM) operated in contact mode. For large force setpoints, single vesicles were either pushed sideways or ruptured by the tip, depending on the tip type (sharp or blunt) used, while for small force setpoints the vesicles were imaged by the tip. To extend the interpretation of and to guide the experiment, we have developed a generic model of the vesicle-tip-substrate system and performed Monte Carlo simulations, addressing the influence of force setpoint and tip speed and shape on the type of imaging or manipulation observed. Specifically, we have explored AFM-image height and width variations versus force setpoint, typical AFM images for small and large force setpoints, tip-induced vesicle strain versus force setpoint, typical vesicle shapes during pushing for different tip speeds, and the details of vesicle rupture induced by the tip.