The influence of shield wires on Geomagnetically Induced Currents (GICs) in power systems is considered. For the most simple power network, with one single transmission line and one shield wire connecting two substations, we derive the expressions for the voltage source and the resistance of the Thévenin equivalent circuits that, in parallel with the substations grounding resistances, produce the same effects on GICs as the full circuit. Our model extends results from previous studies that considered the effect of shield wires resistances by also including the induced geoelectric field.