This paper presents a simple and reliable algorithm for the harmonic analysis of both current and voltage conditions along double-circuit system overhead transmission lines. The developed numerical model is based on the finite element technique which is essential in the process of reducing the problem of solving a complicated system to the problem of solving a subsystem, for which we can easily define a local system of equations based on a mathematical model. To calculate the short-circuit current distribution along the considered double-circuit system overhead transmission lines, it is necessary to divide the entire transmission line into as many finite elements as there are spans between power line towers. It is also necessary to model the grounding of each tower as a separate finite element. An assumed hydroelectric power plant with associated generators and incident network are also shown as separate finite elements with associated parameters. The safety of the maintenance worker on the disconnected and passive circuit of double-circuit overhead transmission line system is directly related to the induced voltages at the worksite. As a worst-case scenario from the standpoint of induced voltages, we considered the case of a single-phase earth fault on the active circuit of a double-circuit overhead transmission line system, where the highest possible single-phase earth fault current value has been taken into account. During this fault, the passive circuit of the double-circuit overhead transmission line system is grounded on both ends of the line. Induced voltages were analyzed in the case of a grounded worksite tower and two adjacent towers along the entire double-circuit system overhead transmission lines system.