The effect of an external electric field on the electromechanical properties and regularities of the resistive switching of a vertically aligned carbon nanotube (VA CNT) has been studied experimentally using scanning tunneling microscopy. It has been shown that the VA CNT resistivity ratio in the high- and low-resistance states is higher than 25 as the distance between the scanning tunneling microscope (STM) probe and the VA CNT is 1 nm at a voltage of 8 V and depends on the voltage applied between the probe and the VA CNT. The proposed mechanism of resistive switching of VA CNTs is based on an instantaneous deformation and induction of a VA CNT internal electric field as a result of the sharp change in the time derivative of the external electric field strength. The obtained results can be used for the design and fabrication of resistive energy-efficient memory elements with a high density of storage cells on the basis of vertically aligned carbon nanotubes.