In this article a novel inspection machine for high-voltage electrical line has been proposed and mathematical modeling issues of its movement along the conductors have been considered. In order to improve the mechanical mechanism and achieve dynamical stability to navigate through overhead electrical transmission lines, variation methods for problems of string have been considered. However, DMAs operation might be subject to failures because of the conductor vibration. Even in the case of slow movement of the machine, intensive vibrations and stipulated by them significant inertial loading might occur. The behavior of the inspection machine while it is traveling through high-voltage electrical transmission lines has been studied.