Carson's equations for computation of frequency dependent parameters of overhead transmission line are modified. The earth is considered to be homogenous. The optimal required number of terms of Carson's series for applications on computer is determined. Accurate mathematical expressions for resistance and inductance of overhead transmission lines are obtained.Different arrangements of conductors for double circuit transmission lines are studied. The mutual inductance and potential coefficient (mutual capacitance) of such arrangements are computed. Double voltage class type double circuit transmission lines are suggested. The plate type double circuit lines are proposed for power transmission over long distances.This paper presents a mathematical analysis in order to determine the coefficients of similarity criteria of EHF physical model for the given long distance transmission line. The integral analogue method and PI-theorem are used. The independent parameters of EHF physical model are formulated. The scales of four independent parameters of the designed EHF physical model are obtained.