The paper describes an analytical method for eddy currents induced in tubular conductors of a system of two parallel tubular conductors by a transverse alternating magnetic field generated by a current in one of them. The skin effect is taken into consideration. The magnetic field is presented by means of a vector magnetic potential as Fourier series. The proposed solution can be used to describe semi-analytically the current density induced due to the proximity effect in high current bus ducts or gas insulated lines (GILs) with tubular conductors. Therefore, the extent of its potential applications is wide, and the considered problem has a practical significance.