Geometrical capacitors with memory (memcapacitors) are of interest because of potential applications in future computing machines. When employing a buckled membrane as one of the capacitor plates, two possible buckled positions serve as the states of low and high capacitance. Using the hybrid B3LYP/6-31G approximation, we investigate the snap-through transition of neutral and negatively charged buckled graphene membranes under the transverse load and external electrostatic field created by a point charge. Estimations show that the chosen calculation method reproduces the elastic properties of graphene within the limits of experimental error. The obtained results testify to the fact that the membrane charge and external electrostatic field affect notably the threshold snap-through switching force in nanosized membranes and, therefore, should be taken into account in the design and development of such nanodevices.