Rigorous analysis of discontinuities in planar transmission lines may require accurate computation of a large number of modes. An improved formulation of the singular integral equation (SIE) method for multilayer unilateral finlines was presented to address this problem. All the series truncated possess the fast convergence property. A systematic approach for analytical calculation of the characteristic matrix to arbitrary order was also proposed. For the determination of propagation constants, an analytical function that eliminates all the poles in the determinant of the characteristic matrix was constructed. The developed numerical techniques lead to an accurate, efficient, and reliable computation of both propagation constants and field distributions for a large number of modes.