Abstract: In this paper, we present an analytical method of the propagation characteristics for the finlines with extremely narrow slotwidths, the effect of fin thickness being taken into account also. The dispersion and impedance characteristics are calculated by the present method for the unilateral and bilateral finlines. The numerical analyses show that the method avoids the convergence problems mob with in computing the finlines with extremely narrow slotwidth by other numerical techniques, and justify that this method possesses the advantages of rapidity, effectiveness and simplicity.