Asymptotic solutions for the surface field due to a magnetic point source on a cylinder can simplify the computational task in the analysis of mutual coupling-e.g. in conformal arrays. Although several asymptotic solutions are at present available, their accuracy is limited. The aim here is to obtain a new approximate solution with improved accuracy. An asymptotic solution of the exact modal solution for the field on a cylinder which contains terms up to (k0t)-2, where t is the distance from the source, is derived. Approximate terms up to (k0t) -3 are included from the solution for a source on a plane conductor and an earlier asymptotic solution. The new approximate solution consists of the exact solution for a plane conductor, modulated by a Fock function, plus a contribution associated with the cylinder which vanishes in the limit of infinite radius. Typically for cylinders of radius greater than one and half wavelengths it agrees to within O.5 dB in magnitude and 1 ° in phase of the modal solution. Results for dominant mode mutual and self-admittances of rectangular apertures on a cylinder obtained from this solution are presented. A formula is also given for calculating self-admittances from an asymptotic solution. There is excellent agreement between admittances computed from the asymptotic solution and the modal solution. One exception is the self-susceptance of an axial slot where the error is larger than expected, although the error is low enough to be acceptable in most practical cases.