A two-dimensional cylindrical, non-uniform finite difference time domain technique is employed in conjunction with an unsplit, anisotropic perfectly matched layer for boundary mesh truncation, for the analysis of printed cylindrical transmission lines. The computed propagation characteristics for both shielded and open structures are found to be in good agreement with the results obtained via the uniform cylindrical FDTD technique. However, the requirements of computation capacity are significantly reduced. It is found that the Gibb's phenomenon corrupts the results, but can be eliminated by using the Blackman-Harris window function to truncate and modulate the time domain signatures.