A new approach, the multipole theory(MT) method, is presented for computation of the characteristics impedance of the rectangular shielded planar striplines. The rectangular structure is transformed as the cylindrical structure by conformal mapping, the inhomogeneous field domain is treated as a combination of several simple homogeneous regions, and the solution of the boundary-value problem is represented by the generalized MT formula. Representative computational examples, including asymmetric TEM cell, rectangular shielded single microstrip line and coupled microstrip line on multilayered substrates, are given to validate the theory, and to demonstrate the accuracy and flexibility of the MT method. Downloaded by [Umeå University Library] at 11:43 17 November 2014 1358 Zheng et al.