Vertical monopoles over an infinite ground plane that are embedded in a dielectric slab are studied using a mixed potential integral equation formulation. The method of moments is used to solve for the induced currents from which impedance parameters are calculated. The vector and scalar potentials are written in terms of Sommerfeld integrals that are evaluated using efficient techniques developed for the analysis of microstrip antennas. A magnetic current frill is used to model the coaxial aperture in the ground plane that excites the monopole. Measured and calculated input impedance and mutual coupling data are compared and a study of the effect of the dielectric inhomogeneity is performed.