Available closed-form Green's function (CFGF) representations for cylindrically stratified media are modified to obtain new CFGF representations that yield very accurate results for cases where source and field points are on the top of or very close to each other. Consequently, these new expressions can safely be used for the entries of the method of moments (MoM) impedance matrix that represent the self and overlapping terms in a Galerkin MoM procedure. Numerical results for the self term and mutual coupling between arbitrarily oriented current modes are obtained using these new CFGF representations and compared with the results of an eigenfunction solution developed using spectral domain techniques. Excellent agreement is achieved.