In this paper, a modal analysis of a rectangular dielectric resonator antenna (DRA), with unconventional boundary conditions, is carried out. Analytical equations of the fields inside the resonator and simulations are presented, showing that if a resonator is mounted over a ground plane and loaded by a top metallic sheet, there is a miniaturization of the electric size of the new antenna, without significant deterioration of performance. Furthermore, dual-band responses can be achieved with this configuration.