This article presents the solution to the heretofore unresolved problem of precise computation for the near field of printed circuits and printed circuit antennas on cylindrical substrates. The procedure involves a recurrence/continued fraction algorithm development for the evaluation of the Green's function pertinent to this particular configuration of printed circuit elements. With this new algorithm, arbitrary size cylindrical substrates can be modelled with an extremely high degree of accuracy. Computation of the input impedance of center fed and axially symmetric microstrip dipoles is used as an example. Excellent agreement is found for large cylinders with the limiting case of center fed microstrip dipoles on planar substrates.