We present an approach for the method of moments (MoM) analysis of antennas of arbitrary shape printed on a cylindrical substrate. We propose several key components of a code to perform this analysis, with the explicit goal of adapting MoM codes devised for planar stratified structures. For that purpose, the background medium Green's function is expressed in the mixed-potential (MP) format to allow for efficient numerical integration; the spectral dyadic Green's function is first recast in the spectral counterpart of the spatial mixed-potential form. The convergence of the spectral-to-spatial transform is accelerated by extraction of spectral asymptotic functions and exploitation of the azimuthal periodicity. Several important issues of implementation, numerical stability, and accuracy are addressed with a view to incorporate the spatial MP Green's function into the MoM analysis of printed structures of arbitrary shape using RWG basis functions. The numerical results are in good agreement with those obtained by other methods and with measured data.