Based on Carson's analysis of opposite directional current in a pair of parallel wires, proximity resistance in case of same directional current of high frequencies ranging from 200kHz to 1MHz was investigated analytically by introduction of a new magnetic factor into the the electro-magnetic interaction between two wires. As a result, the ratio of AC to DC resistance was successfully obtained in accordance with experimental values within 10%. Furthermore, current distribution in the cross section of two wires was calculated and drawn on Cassinian ovals diagram.