Efficient computation of the Fresnel-zone fields for circular apertures plays an important role in applications where the frequency, aperture size, and observation location are such that the Fraunhofer approximation is not justified. If an adequate approximation for the aperture field distribution is known, then the standard procedure for computing the Fresnel-zone field distribution involves a time-consuming numerical integration over the aperture field distribution. In this paper, we will represent the Fresnel-zone field for some commonly used aperture field distributions in terms of incomplete Weber integrals, thereby avoiding the need for numerical integration. Since the incomplete Weber integrals are related to the incomplete Lipschitz-Hankel integration of the first kind, four Bessel series expansions are used to dramatically reduce the computation time required to compute the Fresnel-zone electric fields. ¿ American Geophysical Union 1994