The problem of microstrip annular-ring patch antenna excited by a probe is solved using rigorous analysis. Minimal assumptions, except the uniform current distribution on the probe and zero thickness of the patch have been made in our analysis. By using the vector Hankel transforms, the problem is formulated in terms of vector dual-integral equations, from which the surface current on the patch can be solved for. The singular part of the current arising from the probe feed is extracted from the expansion series in order to accelerate convergence. It is shown that this analysis agrees with the single mode approximation (SMA) method when the substrate layer is thin, while it deviates from the SMA method drastically when the substrates become thick. Experimental results show that the analytical procedure used in this paper can greatly improve the accuracy of the computed input impedance of microstrip annular-ring patch antenna.