Analysis of the higher order TE and TM modes in transverse electromagnetic (TEM) cells and in general for the rectangular coaxial lines (RCL) with finite metalization thickness for the inner conductor is presented using the mode matching method (MMM). The advantage of this method is its straight-forward formulation which leads to a very reliable algorithm for the computation of fundamental and higher order modes and the characteristic impedance. The basic theoretical steps for the MMM are described and results for the higher order modes for all possible symmetries are presented.