The structure of the system consisting of an aspirating pipette and an aspirated vesicle is investigated with fixed total vesicle volume, total vesicle surface area, and aspirated volume fraction, based on the bending-energy model. Through an energetic consideration, the usage of an aspirated volume fraction can be converted to the aspirating pressure for the determination of a phase diagram; the procedure identifies a first-order transition, between a weakly aspirated state and the strongly aspirated state, as the pressure increases. The physical properties of the system are obtained from minimization of the bending energy by an implementation of the simulated annealing Monte Carlo procedure, which searches for a minimum in a multivariable space. An analysis of the hysteresis effects indicates that the experimentally observed aspirating and releasing critical pressures are related to the location of the spinodal points.