Abstract: The electrostatic field region on the cross section of two charged parallel strip transmission lines in a plane is transformed into the interior of a rectangle with the conformal mapping. The capacitance and the electrostatic energy per unit length of the transmission lines are obtained. On the basis of the principle of virtual work, the electrostatic force between the two lines is calculated. Variation of the normalized force verses according to the geometric parameters is illustrated. The typical Special cases are analyzed, including the force between charged strings, narrow lines and broad lines.